Author: "Velhinho, José" / Publication Year Range: Last 10 years - Searchworks@Jio Institute Digital Library Search Results

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91 results on '"Velhinho, José"'

1. Time-dependent scalings and Fock quantization of a massless scalar field in Kantowski-Sachs

Author: Cortez, Jerónimo, Marugán, Guillermo A. Mena, Torres-Caballeros, Alvaro, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We address the issue of inequivalent Fock representations in Quantum Field Theory in a curved homogenous and anisotropic background, namely Kantowski-Sachs spacetime. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.
Published: 2024

2. Topics of Measure Theory on Infinite Dimensional Spaces

Author: Velhinho, José
Subjects: Mathematics - Functional Analysis, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematical Physics
Abstract: This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures. Transformation properties of measures are considered, as well as fundamental results concerning the support of the measure.
Published: 2023
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3. Comments on mathematical aspects of the Bir\'o-N\'eda model

Author: Inácio, Ilda and Velhinho, José
Subjects: Mathematical Physics, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Adaptation and Self-Organizing Systems
Abstract: We address two mathematical aspects of the Bir\'o--N\'eda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions.
Published: 2023
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4. Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

Author: Velhinho, José
Subjects: Mathematical Physics, High Energy Physics - Theory
Abstract: This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing to distinguish between the typical quantum fields associated with different values of the mass.
Published: 2023
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5. Fock quantization of a Klein-Gordon field in the interior geometry of a nonrotating black hole

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Marugán, Guillermo A. Mena, Torres-Caballeros, Alvaro, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type., Comment: 13 pages
Published: 2023

6. A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

Author: Cortez, Jerónimo, Marugán, Guillermo A. Mena, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology, High Energy Physics - Theory
Abstract: The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose some conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections. These symmetries may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction, or with dynamical transformations that in fact are not symmetries. We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization, a demand that can be seen as a weaker version of the requirement of invariance. In particular, a strict invariance under certain transformations may eliminate some physically interesting possibilities in the passage to the quantum theory. This is the first review in which this unified perspective is adopted to discuss otherwise rather different uniqueness criteria proposed either in homogeneous loop quantum cosmology or in the Fock quantization of inhomogeneous cosmologies., Comment: 24 pages
Published: 2021
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7. Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Marugán, Guillermo A. Mena, Prado, Santiago, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in several cosmological spacetimes, and present recent results about well-motivated criteria that ensure the uniqueness in the selection of a vacuum up to unitary transformations. These criteria are based on two requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also determines an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in cosmological spacetimes of 2+1 dimensions and then discuss the more relevant case of 3+1 dimensions. We use this analysis to investigate the hybrid loop quantization of a flat Friedmann-Lema\^itre-Robertson-Walker background cosmology coupled to a perturbative Dirac field. Among the Fock quantizations for the fermionic perturbations allowed by our criteria, we further restrict the choice of vacuum by demanding a finite fermionic backreaction and, moreover, by diagonalizing the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniquess of the vacuum state selected by the extension of this diagonalization condition beyond the ultraviolet regime, proving that it picks out the standard Poincar\'e and Bunch-Davies vacua for fixed flat and de Sitter background spacetimes, respectively., Comment: 48 pages
Published: 2020
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8. Quantum linear scalar fields with time dependent potentials: Overview and applications to cosmology

Author: Cortez, Jerónimo, Marugán, Guillermo A. Mena, and Velhinho, José
Subjects: General Relativity and Quantum Cosmology
Abstract: In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations., Comment: 57 pages
Published: 2019

9. General solutions to decay chain equations

Author: Velhinho, José, Fonseca, Elsa, and Serôdio, Rogério
Published: 2023
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10. Black holes, gravitational waves and fundamental physics: a roadmap

Author: Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P., Askar, Abbas, Belczynski, Krzysztof, Bertone, Gianfranco, Bon, Edi, Blas, Diego, Brito, Richard, Bulik, Tomasz, Burrage, Clare, Byrnes, Christian T., Caprini, Chiara, Chernyakova, Masha, Chrusciel, Piotr, Colpi, Monica, Ferrari, Valeria, Gaggero, Daniele, Gair, Jonathan, Garcia-Bellido, Juan, Hassan, S. F., Heisenberg, Lavinia, Hendry, Martin, Heng, Ik Siong, Herdeiro, Carlos, Hinderer, Tanja, Horesh, Assaf, Kavanagh, Bradley J., Kocsis, Bence, Kramer, Michael, Tiec, Alexandre Le, Mingarelli, Chiara, Nardini, Germano, Nelemans, Gijs, Palenzuela, Carlos, Pani, Paolo, Perego, Albino, Porter, Edward K., Rossi, Elena M., Schmidt, Patricia, Sesana, Alberto, Sperhake, Ulrich, Stamerra, Antonio, Stein, Leo C., Tamanini, Nicola, Tauris, Thomas M., Urena-Lopez, L. Arturo, Vincent, Frederic, Volonteri, Marta, Wardell, Barry, Wex, Norbert, Yagi, Kent, Abdelsalhin, Tiziano, Aloy, Miguel Angel, Amaro-Seoane, Pau, Annulli, Lorenzo, Arca-Sedda, Manuel, Bah, Ibrahima, Barausse, Enrico, Barakovic, Elvis, Benkel, Robert, Bennett, Charles L., Bernard, Laura, Bernuzzi, Sebastiano, Berry, Christopher P. L., Berti, Emanuele, Bezares, Miguel, Blanco-Pillado, Jose Juan, Blazquez-Salcedo, Jose Luis, Bonetti, Matteo, Boskovic, Mateja, Bosnjak, Zeljka, Bricman, Katja, Bruegmann, Bernd, Capelo, Pedro R., Carloni, Sante, Cerda-Duran, Pablo, Charmousis, Christos, Chaty, Sylvain, Clerici, Aurora, Coates, Andrew, Colleoni, Marta, Collodel, Lucas G., Compere, Geoffrey, Cook, William, Cordero-Carrion, Isabel, Correia, Miguel, de la Cruz-Dombriz, Alvaro, Czinner, Viktor G., Destounis, Kyriakos, Dialektopoulos, Kostas, Doneva, Daniela, Dotti, Massimo, Drew, Amelia, Eckner, Christopher, Edholm, James, Emparan, Roberto, Erdem, Recai, Ferreira, Miguel, Ferreira, Pedro G., Finch, Andrew, Font, Jose A., Franchini, Nicola, Fransen, Kwinten, Gal'tsov, Dmitry, Ganguly, Apratim, Gerosa, Davide, Glampedakis, Kostas, Gomboc, Andreja, Goobar, Ariel, Gualtieri, Leonardo, Guendelman, Eduardo, Haardt, Francesco, Harmark, Troels, Hejda, Filip, Hertog, Thomas, Hopper, Seth, Husa, Sascha, Ihanec, Nada, Ikeda, Taishi, Jaodand, Amruta, Jimenez-Forteza, Philippe Jetzer Xisco, Kamionkowski, Marc, Kaplan, David E., Kazantzidis, Stelios, Kimura, Masashi, Kobayashi, Shiho, Kokkotas, Kostas, Krolik, Julian, Kunz, Jutta, Lammerzahl, Claus, Lasky, Paul, Lemos, Jose P. S., Said, Jackson Levi, Liberati, Stefano, Lopes, Jorge, Luna, Raimon, Ma, Yin-Zhe, Maggio, Elisa, Montero, Marina Martinez, Maselli, Andrea, Mayer, Lucio, Mazumdar, Anupam, Messenger, Christopher, Menard, Brice, Minamitsuji, Masato, Moore, Christopher J., Mota, David, Nampalliwar, Sourabh, Nerozzi, Andrea, Nichols, David, Nissimov, Emil, Obergaulinger, Martin, Obers, Niels A., Oliveri, Roberto, Pappas, George, Pasic, Vedad, Peiris, Hiranya, Petrushevska, Tanja, Pollney, Denis, Pratten, Geraint, Rakic, Nemanja, Racz, Istvan, Radia, Miren, Ramazanouglu, Fethi M., Ramos-Buades, Antoni, Raposo, Guilherme, Rosca-Mead, Roxana, Rogatko, Marek, Rosinska, Dorota, Rosswog, Stephan, Morales, Ester Ruiz, Sakellariadou, Mairi, Sanchis-Gual, Nicolas, Salafia, Om Sharan, Samajdar, Anuradha, Sintes, Alicia, Smole, Majda, Sopuerta, Carlos, Souza-Lima, Rafael, Stalevski, Marko, Stergioulas, Nikolaos, Stevens, Chris, Tamfal, Tomas, Torres-Forne, Alejandro, Tsygankov, Sergey, Unluturk, Kivanc, Valiante, Rosa, van de Meent, Maarten, Velhinho, Jose, Verbin, Yosef, Vercnocke, Bert, Vernieri, Daniele, Vicente, Rodrigo, Vitagliano, Vincenzo, Weltman, Amanda, Whiting, Bernard, Williamson, Andrew, Witek, Helvi, Wojnar, Aneta, Yakut, Kadri, Yan, Haopeng, Yazadjiev, Stoycho, Zaharijas, Gabrijela, and Zilhao, Miguel
Subjects: General Relativity and Quantum Cosmology, Astrophysics - High Energy Astrophysical Phenomena, High Energy Physics - Theory
Abstract: The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity
Published: 2018
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11. On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology

Author: Cortez, Jerónimo, Rodrigues, Ilda Inácio, Martín-Benito, Mercedes, and Velhinho, José
Subjects: Mathematical Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory
Abstract: The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the non-stationarity of the spacetime. For the case of a scalar field in cosmological scenarios it is known that the criterion of unitary implementation of the dynamics serves to remove the ambiguity in the choice of Fock representation (up to unitary equivalence). Here, applying the same type of arguments and methods previously used for the scalar field case, we discuss the issue of the uniqueness of the Fock quantization of the Dirac field in the closed FRW spacetime proposed by D'Eath and Halliwell., Comment: 11 pages
Published: 2018
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12. Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Martín-Benito, Mercedes, Marugán, Guillermo A. Mena, Olmedo, Javier, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology., Comment: 23 pages. Updated to match published version
Published: 2016
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13. Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Martín-Benito, Mercedes, Marugán, Guillermo A. Mena, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed., Comment: 19 pages, submitted for publication to Annals of Physics
Published: 2016
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14. Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Martín-Benito, Mercedes, Marugán, Guillermo A. Mena, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in non-stationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obtains an essentially unique splitting of the time variation of the Dirac field into an explicit dependence on the background scale factor and a quantum evolution of the corresponding creation and annihilation operators., Comment: 24 pages. Document replaced to match published version
Published: 2016
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15. Unique Fock quantization of a massive fermion field in a cosmological scenario

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Martín-Benito, Mercedes, Marugán, Guillermo A. Mena, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive to this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a non trivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set., Comment: 21 pages. V2: Updated to match published version
Published: 2016
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16. Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

Author: Cortez, Jerónimo, Navascués, Beatriz Elizaga, Martín-Benito, Mercedes, Marugán, Guillermo A. Mena, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary implementation of the dynamics. When quantizing free scalar fields in homogeneous and isotropic spacetimes with compact spatial sections, these criteria have been shown to pick out a unique Fock representation (up to unitary equivalence). Here, we employ the same criteria for fermion fields and explore whether that uniqueness result can be extended to the case of the Fock quantization of fermions. For the massive Dirac field, we start by introducing a specific choice of the complex structure that determines the Fock representation. Such structure is invariant under the symmetries of the equations of motion. We then prove that the corresponding representation of the canonical anticommutation relations admits a unitary implementation of the dynamics. Moreover, we construct a rather general class of representations that satisfy the above criteria, and we demonstrate that they are all unitarily equivalent to our previous choice. The complex structures in this class are restricted only by certain conditions on their asymptotic behavior for modes in the ultraviolet sector of the Dirac operator. We finally show that, if one assumes that these asymptotic conditions are in fact trivial once our criteria are fulfilled, then the time-dependent scaling in the definition of the fermionic annihilation and creation-like variables is essentially unique., Comment: 24 pages
Published: 2015
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17. Quantum unitary dynamics in cosmological spacetimes

Author: Cortez, Jeronimo, Marugan, Guillermo A. Mena, and Velhinho, Jose M.
Subjects: General Relativity and Quantum Cosmology
Abstract: We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent., Comment: 18 pages
Published: 2015

18. Fock Quantization of a Klein–Gordon Field in the Interior Geometry of a Nonrotating Black Hole

Author: Cortez, Jerónimo, primary, Elizaga Navascués, Beatriz, additional, Mena Marugán, Guillermo A., additional, Torres-Caballeros, Álvaro, additional, and Velhinho, José, additional
Published: 2023
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19. Comments on Mathematical Aspects of the Biró–Néda Model

Author: Inácio, Ilda, primary and Velhinho, José, additional
Published: 2022
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20. A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

Author: Cortez, Jerónimo, primary, Mena Marugán, Guillermo A., additional, and Velhinho, José M., additional
Published: 2021
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21. A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

Author: Ministerio de Ciencia, Innovación y Universidades (España), Agencia Estatal de Investigación (España), European Cooperation in Science and Technology, Fundação para a Ciência e a Tecnologia (Portugal), European Commission, Cortez, Jerónimo, Mena Marugán, Guillermo A., Velhinho, José M., Ministerio de Ciencia, Innovación y Universidades (España), Agencia Estatal de Investigación (España), European Cooperation in Science and Technology, Fundação para a Ciência e a Tecnologia (Portugal), European Commission, Cortez, Jerónimo, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: The purpose of this review is to provide a brief overview of recent conceptual developments regarding possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose certain conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections. These symmetries may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction or with dynamical transformations that are, in fact, not symmetries. We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization—a demand that can be seen as a weaker version of the requirement of invariance. In particular, a strict invariance under certain transformations may eliminate some physically interesting possibilities in the passage to the quantum theory. This is the first review in which this unified perspective is adopted to discuss otherwise different uniqueness criteria proposed either in homogeneous loop quantum cosmology or in the Fock quantization of inhomogeneous cosmologies.
Published: 2021

22. Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Author: Cortez, Jerónimo, primary, Navascués, Beatriz Elizaga, additional, Mena Marugán, Guillermo A., additional, Prado, Santiago, additional, and Velhinho, José M., additional
Published: 2020
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23. Black holes, gravitational waves and fundamental physics

Author: Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P., and Velhinho, José
Abstract: Este relatório foi elaborado no âmbito da European Action on “Black holes, Gravitational waves and Fundamental Physics", que para além dos quatro editores, conta com a participação de inúmeros autores entre eles o Professor Doutor José Velhinho. Submitted by VELHINHO (jvelhi@ubi.pt) on 2019-10-29T10:01:18Z No. of bitstreams: 1 1806.05195.pdf: 7345258 bytes, checksum: cf181eef9e5f5bea7c07f70490cab736 (MD5) Approved for entry into archive by Pessoa (pfep@ubi.pt) on 2019-10-29T10:36:46Z (GMT) No. of bitstreams: 1 1806.05195.pdf: 7345258 bytes, checksum: cf181eef9e5f5bea7c07f70490cab736 (MD5) Approved for entry into archive by Pessoa (pfep@ubi.pt) on 2019-10-29T10:55:30Z (GMT) No. of bitstreams: 1 1806.05195.pdf: 7345258 bytes, checksum: cf181eef9e5f5bea7c07f70490cab736 (MD5) Made available in DSpace on 2019-10-29T10:55:30Z (GMT). No. of bitstreams: 1 1806.05195.pdf: 7345258 bytes, checksum: cf181eef9e5f5bea7c07f70490cab736 (MD5) Previous issue date: 2019-06 info:eu-repo/semantics/publishedVersion
Published: 2019

24. Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Author: Ministerio de Economía y Competitividad (España), European Cooperation in Science and Technology, Universidad Nacional Autónoma de México, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Mena Marugán, Guillermo A., Prado, Santiago, Velhinho, José M., Ministerio de Economía y Competitividad (España), European Cooperation in Science and Technology, Universidad Nacional Autónoma de México, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Mena Marugán, Guillermo A., Prado, Santiago, and Velhinho, José M.
Abstract: In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contri
Published: 2020

25. Quantum linear scalar fields with time dependent potentials: Overview and applications to cosmology

Author: Ministerio de Economía y Competitividad (España), Universidad Nacional Autónoma de México, European Cooperation in Science and Technology, Cortez, Jerónimo, Mena Marugán, Guillermo A., Velhinho, José M., Ministerio de Economía y Competitividad (España), Universidad Nacional Autónoma de México, European Cooperation in Science and Technology, Cortez, Jerónimo, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lemaitre-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations.
Published: 2020

26. Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

Author: Loop quantum gravity, Ministerio de Ciencia, Innovación y Universidades (España), European Commission, Cortez, Jerónimo, Navascués, Beatriz Elizaga, Mena Marugán, Guillermo A., Prado, Santiago, Velhinho, José M., Loop quantum gravity, Ministerio de Ciencia, Innovación y Universidades (España), European Commission, Cortez, Jerónimo, Navascués, Beatriz Elizaga, Mena Marugán, Guillermo A., Prado, Santiago, and Velhinho, José M.
Abstract: In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in non-stationary spacetimes, and present recent results obtained by us and our collaborators about well-motivated criteria capable to ensure the uniqueness in the selection of a vacuum up to unitary transformations, at least in certain situations of interest in cosmology. These criteria are based on two reasonable requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. These symmetries include the spatial isometries. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also allows us to determine an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in 2 + 1 dimensions and then discuss the more relevant case of 3 + 1 dimensions, particularizing the analysis to cosmological spacetimes with spatial sections of spherical or toroidal topology. We use this analysis to investigate the combined, hybrid quantization of the Dirac field and a flat homogeneous and isotropic background cosmology when the latter is treated as a quantum entity, and the former as a perturbation. Specifically, we focus our study on a background quantization along the lines of loop quantum cosmology. Among the Fock quantizations for the fermionic perturbations admissible according to our criteria, we discuss the possibility of further restricting the choice of a vacuum by the requisite of a finite fermionic backreaction and, moreover, by the diagonalization of the fermionic contri
Published: 2020

27. Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology

Author: Cortez, Jerónimo, primary, Mena Marugán, Guillermo A., additional, and Velhinho, José, additional
Published: 2020
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28. Black holes, gravitational waves and fundamental physics: a roadmap

Author: Barack, Leor, primary, Cardoso, Vitor, additional, Nissanke, Samaya, additional, Sotiriou, Thomas P, additional, Askar, Abbas, additional, Belczynski, Chris, additional, Bertone, Gianfranco, additional, Bon, Edi, additional, Blas, Diego, additional, Brito, Richard, additional, Bulik, Tomasz, additional, Burrage, Clare, additional, Byrnes, Christian T, additional, Caprini, Chiara, additional, Chernyakova, Masha, additional, Chruściel, Piotr, additional, Colpi, Monica, additional, Ferrari, Valeria, additional, Gaggero, Daniele, additional, Gair, Jonathan, additional, García-Bellido, Juan, additional, Hassan, S F, additional, Heisenberg, Lavinia, additional, Hendry, Martin, additional, Heng, Ik Siong, additional, Herdeiro, Carlos, additional, Hinderer, Tanja, additional, Horesh, Assaf, additional, Kavanagh, Bradley J, additional, Kocsis, Bence, additional, Kramer, Michael, additional, Le Tiec, Alexandre, additional, Mingarelli, Chiara, additional, Nardini, Germano, additional, Nelemans, Gijs, additional, Palenzuela, Carlos, additional, Pani, Paolo, additional, Perego, Albino, additional, Porter, Edward K, additional, Rossi, Elena M, additional, Schmidt, Patricia, additional, Sesana, Alberto, additional, Sperhake, Ulrich, additional, Stamerra, Antonio, additional, Stein, Leo C, additional, Tamanini, Nicola, additional, Tauris, Thomas M, additional, Urena-López, L Arturo, additional, Vincent, Frederic, additional, Volonteri, Marta, additional, Wardell, Barry, additional, Wex, Norbert, additional, Yagi, Kent, additional, Abdelsalhin, Tiziano, additional, Aloy, Miguel Ángel, additional, Amaro-Seoane, Pau, additional, Annulli, Lorenzo, additional, Arca-Sedda, Manuel, additional, Bah, Ibrahima, additional, Barausse, Enrico, additional, Barakovic, Elvis, additional, Benkel, Robert, additional, Bennett, Charles L, additional, Bernard, Laura, additional, Bernuzzi, Sebastiano, additional, Berry, Christopher P L, additional, Berti, Emanuele, additional, Bezares, Miguel, additional, Blanco-Pillado, Jose Juan, additional, Blázquez-Salcedo, Jose Luis, additional, Bonetti, Matteo, additional, Bošković, Mateja, additional, Bosnjak, Zeljka, additional, Bricman, Katja, additional, Brügmann, Bernd, additional, Capelo, Pedro R, additional, Carloni, Sante, additional, Cerdá-Durán, Pablo, additional, Charmousis, Christos, additional, Chaty, Sylvain, additional, Clerici, Aurora, additional, Coates, Andrew, additional, Colleoni, Marta, additional, Collodel, Lucas G, additional, Compère, Geoffrey, additional, Cook, William, additional, Cordero-Carrión, Isabel, additional, Correia, Miguel, additional, de la Cruz-Dombriz, Álvaro, additional, Czinner, Viktor G, additional, Destounis, Kyriakos, additional, Dialektopoulos, Kostas, additional, Doneva, Daniela, additional, Dotti, Massimo, additional, Drew, Amelia, additional, Eckner, Christopher, additional, Edholm, James, additional, Emparan, Roberto, additional, Erdem, Recai, additional, Ferreira, Miguel, additional, Ferreira, Pedro G, additional, Finch, Andrew, additional, Font, Jose A, additional, Franchini, Nicola, additional, Fransen, Kwinten, additional, Gal’tsov, Dmitry, additional, Ganguly, Apratim, additional, Gerosa, Davide, additional, Glampedakis, Kostas, additional, Gomboc, Andreja, additional, Goobar, Ariel, additional, Gualtieri, Leonardo, additional, Guendelman, Eduardo, additional, Haardt, Francesco, additional, Harmark, Troels, additional, Hejda, Filip, additional, Hertog, Thomas, additional, Hopper, Seth, additional, Husa, Sascha, additional, Ihanec, Nada, additional, Ikeda, Taishi, additional, Jaodand, Amruta, additional, Jetzer, Philippe, additional, Jimenez-Forteza, Xisco, additional, Kamionkowski, Marc, additional, Kaplan, David E, additional, Kazantzidis, Stelios, additional, Kimura, Masashi, additional, Kobayashi, Shiho, additional, Kokkotas, Kostas, additional, Krolik, Julian, additional, Kunz, Jutta, additional, Lämmerzahl, Claus, additional, Lasky, Paul, additional, Lemos, José P S, additional, Levi Said, Jackson, additional, Liberati, Stefano, additional, Lopes, Jorge, additional, Luna, Raimon, additional, Ma, Yin-Zhe, additional, Maggio, Elisa, additional, Mangiagli, Alberto, additional, Montero, Marina Martinez, additional, Maselli, Andrea, additional, Mayer, Lucio, additional, Mazumdar, Anupam, additional, Messenger, Christopher, additional, Ménard, Brice, additional, Minamitsuji, Masato, additional, Moore, Christopher J, additional, Mota, David, additional, Nampalliwar, Sourabh, additional, Nerozzi, Andrea, additional, Nichols, David, additional, Nissimov, Emil, additional, Obergaulinger, Martin, additional, Obers, Niels A, additional, Oliveri, Roberto, additional, Pappas, George, additional, Pasic, Vedad, additional, Peiris, Hiranya, additional, Petrushevska, Tanja, additional, Pollney, Denis, additional, Pratten, Geraint, additional, Rakic, Nemanja, additional, Racz, Istvan, additional, Radia, Miren, additional, Ramazanoğlu, Fethi M, additional, Ramos-Buades, Antoni, additional, Raposo, Guilherme, additional, Rogatko, Marek, additional, Rosca-Mead, Roxana, additional, Rosinska, Dorota, additional, Rosswog, Stephan, additional, Ruiz-Morales, Ester, additional, Sakellariadou, Mairi, additional, Sanchis-Gual, Nicolás, additional, Sharan Salafia, Om, additional, Samajdar, Anuradha, additional, Sintes, Alicia, additional, Smole, Majda, additional, Sopuerta, Carlos, additional, Souza-Lima, Rafael, additional, Stalevski, Marko, additional, Stergioulas, Nikolaos, additional, Stevens, Chris, additional, Tamfal, Tomas, additional, Torres-Forné, Alejandro, additional, Tsygankov, Sergey, additional, İ Ünlütürk, Kıvanç, additional, Valiante, Rosa, additional, van de Meent, Maarten, additional, Velhinho, José, additional, Verbin, Yosef, additional, Vercnocke, Bert, additional, Vernieri, Daniele, additional, Vicente, Rodrigo, additional, Vitagliano, Vincenzo, additional, Weltman, Amanda, additional, Whiting, Bernard, additional, Williamson, Andrew, additional, Witek, Helvi, additional, Wojnar, Aneta, additional, Yakut, Kadri, additional, Yan, Haopeng, additional, Yazadjiev, Stoycho, additional, Zaharijas, Gabrijela, additional, and Zilhão, Miguel, additional
Published: 2019
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29. Black holes, gravitational waves and fundamental physics : a roadmap

Author: Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P., Askar, Abbas, Belczynski, Chris, Bertone, Gianfranco, Bon, Edi, Blas, Diego, Brito, Richard, Bulik, Tomasz, Burrage, Clare, Byrnes, Christian T., Caprini, Chiara, Chernyakova, Masha, Chruściel, Piotr, Colpi, Monica, Ferrari, Valeria, Gaggero, Daniele, Gair, Jonathan, García-Bellido, Juan, Hassan, Sayed Fawad, Heisenberg, Lavinia, Hendry, Martin, Heng, Ik Siong, Herdeiro, Carlos, Hinderer, Tanja, Horesh, Assaf, Kavanagh, Bradley J., Kocsis, Bence, Kramer, Michael, Le Tiec, Alexandre, Mingarelli, Chiara, Nardini, Germano, Nelemans, Gijs, Palenzuela, Carlos, Pani, Paolo, Perego, Albino, Porter, Edward K., Rossi, Elena M., Schmidt, Patricia, Sesana, Alberto, Sperhake, Ulrich, Stamerra, Antonio, Stein, Leo C., Tamanini, Nicola, Tauris, Thomas M., Arturo Urena-López, L., Vincent, Frederic, Volonteri, Marta, Wardell, Barry, Wex, Norbert, Yagi, Kent, Abdelsalhin, Tiziano, Ángel Aloy, Miguel, Amaro-Seoane, Pau, Annulli, Lorenzo, Arca-Sedda, Manuel, Bah, Ibrahima, Barausse, Enrico, Barakovic, Elvis, Benkel, Robert, Bennett, Charles L., Bernard, Laura, Bernuzzi, Sebastiano, Berry, Christopher P. L., Berti, Emanuele, Bezares, Miguel, Juan Blanco-Pillado, Jose, Blázquez-Salcedo, Jose Luis, Bonetti, Matteo, Bošković, Mateja, Bosnjak, Zeljka, Bricman, Katja, Brügmann, Bernd, Capelo, Pedro R., Carloni, Sante, Cerdá-Durán, Pablo, Charmousis, Christos, Chaty, Sylvain, Clerici, Aurora, Coates, Andrew, Colleoni, Marta, Collodel, Lucas G., Compère, Geoffrey, Cook, William, Cordero-Carríon, Isabel, Correia, Miguel, de la Cruz-Dombriz, Álvaro, Czinner, Viktor G., Destounis, Kyriakos, Dialektopoulos, Kostas, Doneva, Daniela, Dotti, Massimo, Drew, Amelia, Eckner, Christopher, Edholm, James, Emparan, Roberto, Erdem, Recai, Ferreira, Miguel, Ferreira, Pedro G., Finch, Andrew, Font, Jose A., Franchini, Nicola, Fransen, Kwinten, Gal'tsov, Dmitry, Ganguly, Apratim, Gerosa, Davide, Glampedakis, Kostas, Gomboc, Andreja, Goobar, Ariel, Gualtieri, Leonardo, Guendelman, Eduardo, Haardt, Francesco, Harmark, Troels, Hejda, Filip, Hertog, Thomas, Hopper, Seth, Husa, Sascha, Ihanec, Nada, Ikeda, Taishi, Jaodand, Amruta, Jetzer, Philippe, Jimenez-Forteza, Xisco, Kamionkowski, Marc, Kaplan, David E., Kazantzidis, Stelios, Kimura, Masashi, Kobayashi, Shiho, Kokkotas, Kostas, Krolik, Julian, Kunz, Jutta, Lämmerzahl, Claus, Lasky, Paul, Lemos, José P. S., Said, Jackson Levi, Liberati, Stefano, Lopes, Jorge, Luna, Raimon, Ma, Yin-Zhe, Maggio, Elisa, Mangiagli, Alberto, Montero, Marina Martinez, Maselli, Andrea, Mayer, Lucio, Mazumdar, Anupam, Messenger, Christopher, Ménard, Brice, Minamitsuji, Masato, Moore, Christopher J., Mota, David, Nampalliwar, Sourabh, Nerozzi, Andrea, Nichols, David, Nissimov, Emil, Obergaulinger, Martin, Obers, Niels A., Oliveri, Roberto, Pappas, George, Pasic, Vedad, Peiris, Hiranya, Petrushevska, Tanja, Pollney, Denis, Pratten, Geraint, Rakic, Nemanja, Racz, Istvan, Radia, Miren, Ramazanoglu, Fethi M., Ramos-Buades, Antoni, Raposo, Guilherme, Rogatko, Marek, Rosca-Mead, Roxana, Rosinska, Dorota, Rosswog, Stephan, Ruiz-Morales, Ester, Sakellariadou, Mairi, Sanchis-Gual, Nicolás, Salafia, Om Sharan, Samajdar, Anuradha, Sintes, Alicia, Smole, Majda, Sopuerta, Carlos, Souza-Lima, Rafael, Stalevski, Marko, Stergioulas, Nikolaos, Stevens, Chris, Tamfal, Tomas, Torres-Forne, Alejandro, Tsygankov, Sergey, Ünlütürk, Kivanç I., Valiante, Rosa, van de Meent, Maarten, Velhinho, José, Verbin, Yosef, Vercnocke, Bert, Vernieri, Daniele, Vicente, Rodrigo, Vitagliano, Vincenzo, Weltman, Amanda, Whiting, Bernard, Williamson, Andrew, Witek, Helvi, Wojnar, Aneta, Yakut, Kadri, Yan, Haopeng, Yazadjiev, Stoycho, Zaharijas, Gabrijela, Zilhão, Miguel, Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P., Askar, Abbas, Belczynski, Chris, Bertone, Gianfranco, Bon, Edi, Blas, Diego, Brito, Richard, Bulik, Tomasz, Burrage, Clare, Byrnes, Christian T., Caprini, Chiara, Chernyakova, Masha, Chruściel, Piotr, Colpi, Monica, Ferrari, Valeria, Gaggero, Daniele, Gair, Jonathan, García-Bellido, Juan, Hassan, Sayed Fawad, Heisenberg, Lavinia, Hendry, Martin, Heng, Ik Siong, Herdeiro, Carlos, Hinderer, Tanja, Horesh, Assaf, Kavanagh, Bradley J., Kocsis, Bence, Kramer, Michael, Le Tiec, Alexandre, Mingarelli, Chiara, Nardini, Germano, Nelemans, Gijs, Palenzuela, Carlos, Pani, Paolo, Perego, Albino, Porter, Edward K., Rossi, Elena M., Schmidt, Patricia, Sesana, Alberto, Sperhake, Ulrich, Stamerra, Antonio, Stein, Leo C., Tamanini, Nicola, Tauris, Thomas M., Arturo Urena-López, L., Vincent, Frederic, Volonteri, Marta, Wardell, Barry, Wex, Norbert, Yagi, Kent, Abdelsalhin, Tiziano, Ángel Aloy, Miguel, Amaro-Seoane, Pau, Annulli, Lorenzo, Arca-Sedda, Manuel, Bah, Ibrahima, Barausse, Enrico, Barakovic, Elvis, Benkel, Robert, Bennett, Charles L., Bernard, Laura, Bernuzzi, Sebastiano, Berry, Christopher P. L., Berti, Emanuele, Bezares, Miguel, Juan Blanco-Pillado, Jose, Blázquez-Salcedo, Jose Luis, Bonetti, Matteo, Bošković, Mateja, Bosnjak, Zeljka, Bricman, Katja, Brügmann, Bernd, Capelo, Pedro R., Carloni, Sante, Cerdá-Durán, Pablo, Charmousis, Christos, Chaty, Sylvain, Clerici, Aurora, Coates, Andrew, Colleoni, Marta, Collodel, Lucas G., Compère, Geoffrey, Cook, William, Cordero-Carríon, Isabel, Correia, Miguel, de la Cruz-Dombriz, Álvaro, Czinner, Viktor G., Destounis, Kyriakos, Dialektopoulos, Kostas, Doneva, Daniela, Dotti, Massimo, Drew, Amelia, Eckner, Christopher, Edholm, James, Emparan, Roberto, Erdem, Recai, Ferreira, Miguel, Ferreira, Pedro G., Finch, Andrew, Font, Jose A., Franchini, Nicola, Fransen, Kwinten, Gal'tsov, Dmitry, Ganguly, Apratim, Gerosa, Davide, Glampedakis, Kostas, Gomboc, Andreja, Goobar, Ariel, Gualtieri, Leonardo, Guendelman, Eduardo, Haardt, Francesco, Harmark, Troels, Hejda, Filip, Hertog, Thomas, Hopper, Seth, Husa, Sascha, Ihanec, Nada, Ikeda, Taishi, Jaodand, Amruta, Jetzer, Philippe, Jimenez-Forteza, Xisco, Kamionkowski, Marc, Kaplan, David E., Kazantzidis, Stelios, Kimura, Masashi, Kobayashi, Shiho, Kokkotas, Kostas, Krolik, Julian, Kunz, Jutta, Lämmerzahl, Claus, Lasky, Paul, Lemos, José P. S., Said, Jackson Levi, Liberati, Stefano, Lopes, Jorge, Luna, Raimon, Ma, Yin-Zhe, Maggio, Elisa, Mangiagli, Alberto, Montero, Marina Martinez, Maselli, Andrea, Mayer, Lucio, Mazumdar, Anupam, Messenger, Christopher, Ménard, Brice, Minamitsuji, Masato, Moore, Christopher J., Mota, David, Nampalliwar, Sourabh, Nerozzi, Andrea, Nichols, David, Nissimov, Emil, Obergaulinger, Martin, Obers, Niels A., Oliveri, Roberto, Pappas, George, Pasic, Vedad, Peiris, Hiranya, Petrushevska, Tanja, Pollney, Denis, Pratten, Geraint, Rakic, Nemanja, Racz, Istvan, Radia, Miren, Ramazanoglu, Fethi M., Ramos-Buades, Antoni, Raposo, Guilherme, Rogatko, Marek, Rosca-Mead, Roxana, Rosinska, Dorota, Rosswog, Stephan, Ruiz-Morales, Ester, Sakellariadou, Mairi, Sanchis-Gual, Nicolás, Salafia, Om Sharan, Samajdar, Anuradha, Sintes, Alicia, Smole, Majda, Sopuerta, Carlos, Souza-Lima, Rafael, Stalevski, Marko, Stergioulas, Nikolaos, Stevens, Chris, Tamfal, Tomas, Torres-Forne, Alejandro, Tsygankov, Sergey, Ünlütürk, Kivanç I., Valiante, Rosa, van de Meent, Maarten, Velhinho, José, Verbin, Yosef, Vercnocke, Bert, Vernieri, Daniele, Vicente, Rodrigo, Vitagliano, Vincenzo, Weltman, Amanda, Whiting, Bernard, Williamson, Andrew, Witek, Helvi, Wojnar, Aneta, Yakut, Kadri, Yan, Haopeng, Yazadjiev, Stoycho, Zaharijas, Gabrijela, and Zilhão, Miguel
Abstract: The grand challenges of contemporary fundamental physics dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.
Published: 2019
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30. Black holes, gravitational waves and fundamental physics: A roadmap

Author: Barack, L, Cardoso, V, Nissanke, S, Sotiriou, T, Askar, A, Belczynski, C, Bertone, G, Bon, E, Blas, D, Brito, R, Bulik, T, Burrage, C, Byrnes, C, Caprini, C, Chernyakova, M, Chruściel, P, Colpi, M, Ferrari, V, Gaggero, D, Gair, J, García-Bellido, J, Hassan, S, Heisenberg, L, Hendry, M, Heng, I, Herdeiro, C, Hinderer, T, Horesh, A, Kavanagh, B, Kocsis, B, Kramer, M, Le Tiec, A, Mingarelli, C, Nardini, G, Nelemans, G, Palenzuela, C, Pani, P, Perego, A, Porter, E, Rossi, E, Schmidt, P, Sesana, A, Sperhake, U, Stamerra, A, Stein, L, Tamanini, N, Tauris, T, Urena-López, L, Vincent, F, Volonteri, M, Wardell, B, Wex, N, Yagi, K, Abdelsalhin, T, Aloy, M, Amaro-Seoane, P, Annulli, L, Arca-Sedda, M, Bah, I, Barausse, E, Barakovic, E, Benkel, R, Bennett, C, Bernard, L, Bernuzzi, S, Berry, C, Berti, E, Bezares, M, Blanco-Pillado, J, Blázquez-Salcedo, J, Bonetti, M, Bošković, M, Bosnjak, Z, Bricman, K, Brügmann, B, Capelo, P, Carloni, S, Cerdá-Durán, P, Charmousis, C, Chaty, S, Clerici, A, Coates, A, Colleoni, M, Collodel, L, Compère, G, Cook, W, Cordero-Carrión, I, Correia, M, de la Cruz-Dombriz, Á, Czinner, V, Destounis, K, Dialektopoulos, K, Doneva, D, Dotti, M, Drew, A, Eckner, C, Edholm, J, Emparan, R, Erdem, R, Ferreira, M, Ferreira, P, Finch, A, Font, J, Franchini, N, Fransen, K, Gal’Tsov, D, Ganguly, A, Gerosa, D, Glampedakis, K, Gomboc, A, Goobar, A, Gualtieri, L, Guendelman, E, Haardt, F, Harmark, T, Hejda, F, Hertog, T, Hopper, S, Husa, S, Ihanec, N, Ikeda, T, Jaodand, A, Jetzer, P, Jimenez-Forteza, X, Kamionkowski, M, Kaplan, D, Kazantzidis, S, Kimura, M, Kobayashi, S, Kokkotas, K, Krolik, J, Kunz, J, Lämmerzahl, C, Lasky, P, Lemos, J, Levi Said, J, Liberati, S, Lopes, J, Luna, R, Ma, Y, Maggio, E, Mangiagli, A, Montero, M, Maselli, A, Mayer, L, Mazumdar, A, Messenger, C, Ménard, B, Minamitsuji, M, Moore, C, Mota, D, Nampalliwar, S, Nerozzi, A, Nichols, D, Nissimov, E, Obergaulinger, M, Obers, N, Oliveri, R, Pappas, G, Pasic, V, Peiris, H, Petrushevska, T, Pollney, D, Pratten, G, Rakic, N, Racz, I, Radia, M, Ramazanoğlu, F, Ramos-Buades, A, Raposo, G, Rogatko, M, Rosca-Mead, R, Rosinska, D, Rosswog, S, Ruiz-Morales, E, Sakellariadou, M, Sanchis-Gual, N, Sharan Salafia, O, Samajdar, A, Sintes, A, Smole, M, Sopuerta, C, Souza-Lima, R, Stalevski, M, Stergioulas, N, Stevens, C, Tamfal, T, Torres-Forné, A, Tsygankov, S, İ Ünlütürk, K, Valiante, R, van de Meent, M, Velhinho, J, Verbin, Y, Vercnocke, B, Vernieri, D, Vicente, R, Vitagliano, V, Weltman, A, Whiting, B, Williamson, A, Witek, H, Wojnar, A, Yakut, K, Yan, H, Yazadjiev, S, Zaharijas, G, Zilhão, M, Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P, Askar, Abbas, Belczynski, Chris, Bertone, Gianfranco, Bon, Edi, Blas, Diego, Brito, Richard, Bulik, Tomasz, Burrage, Clare, Byrnes, Christian T, Caprini, Chiara, Chernyakova, Masha, Chruściel, Piotr, Colpi, Monica, Ferrari, Valeria, Gaggero, Daniele, Gair, Jonathan, García-Bellido, Juan, Hassan, S F, Heisenberg, Lavinia, Hendry, Martin, Heng, Ik Siong, Herdeiro, Carlos, Hinderer, Tanja, Horesh, Assaf, Kavanagh, Bradley J, Kocsis, Bence, Kramer, Michael, Le Tiec, Alexandre, Mingarelli, Chiara, Nardini, Germano, Nelemans, Gijs, Palenzuela, Carlos, Pani, Paolo, Perego, Albino, Porter, Edward K, Rossi, Elena M, Schmidt, Patricia, Sesana, Alberto, Sperhake, Ulrich, Stamerra, Antonio, Stein, Leo C, Tamanini, Nicola, Tauris, Thomas M, Urena-López, L Arturo, Vincent, Frederic, Volonteri, Marta, Wardell, Barry, Wex, Norbert, Yagi, Kent, Abdelsalhin, Tiziano, Aloy, Miguel Ángel, Amaro-Seoane, Pau, Annulli, Lorenzo, Arca-Sedda, Manuel, Bah, Ibrahima, Barausse, Enrico, Barakovic, Elvis, Benkel, Robert, Bennett, Charles L, Bernard, Laura, Bernuzzi, Sebastiano, Berry, Christopher P L, Berti, Emanuele, Bezares, Miguel, Blanco-Pillado, Jose Juan, Blázquez-Salcedo, Jose Luis, Bonetti, Matteo, Bošković, Mateja, Bosnjak, Zeljka, Bricman, Katja, Brügmann, Bernd, Capelo, Pedro R, Carloni, Sante, Cerdá-Durán, Pablo, Charmousis, Christos, Chaty, Sylvain, Clerici, Aurora, Coates, Andrew, Colleoni, Marta, Collodel, Lucas G, Compère, Geoffrey, Cook, William, Cordero-Carrión, Isabel, Correia, Miguel, de la Cruz-Dombriz, Álvaro, Czinner, Viktor G, Destounis, Kyriakos, Dialektopoulos, Kostas, Doneva, Daniela, Dotti, Massimo, Drew, Amelia, Eckner, Christopher, Edholm, James, Emparan, Roberto, Erdem, Recai, Ferreira, Miguel, Ferreira, Pedro G, Finch, Andrew, Font, Jose A, Franchini, Nicola, Fransen, Kwinten, Gal’tsov, Dmitry, Ganguly, Apratim, Gerosa, Davide, Glampedakis, Kostas, Gomboc, Andreja, Goobar, Ariel, Gualtieri, Leonardo, Guendelman, Eduardo, Haardt, Francesco, Harmark, Troels, Hejda, Filip, Hertog, Thomas, Hopper, Seth, Husa, Sascha, Ihanec, Nada, Ikeda, Taishi, Jaodand, Amruta, Jetzer, Philippe, Jimenez-Forteza, Xisco, Kamionkowski, Marc, Kaplan, David E, Kazantzidis, Stelios, Kimura, Masashi, Kobayashi, Shiho, Kokkotas, Kostas, Krolik, Julian, Kunz, Jutta, Lämmerzahl, Claus, Lasky, Paul, Lemos, José P S, Levi Said, Jackson, Liberati, Stefano, Lopes, Jorge, Luna, Raimon, Ma, Yin-Zhe, Maggio, Elisa, Mangiagli, Alberto, Montero, Marina Martinez, Maselli, Andrea, Mayer, Lucio, Mazumdar, Anupam, Messenger, Christopher, Ménard, Brice, Minamitsuji, Masato, Moore, Christopher J, Mota, David, Nampalliwar, Sourabh, Nerozzi, Andrea, Nichols, David, Nissimov, Emil, Obergaulinger, Martin, Obers, Niels A, Oliveri, Roberto, Pappas, George, Pasic, Vedad, Peiris, Hiranya, Petrushevska, Tanja, Pollney, Denis, Pratten, Geraint, Rakic, Nemanja, Racz, Istvan, Radia, Miren, Ramazanoğlu, Fethi M, Ramos-Buades, Antoni, Raposo, Guilherme, Rogatko, Marek, Rosca-Mead, Roxana, Rosinska, Dorota, Rosswog, Stephan, Ruiz-Morales, Ester, Sakellariadou, Mairi, Sanchis-Gual, Nicolás, Sharan Salafia, Om, Samajdar, Anuradha, Sintes, Alicia, Smole, Majda, Sopuerta, Carlos, Souza-Lima, Rafael, Stalevski, Marko, Stergioulas, Nikolaos, Stevens, Chris, Tamfal, Tomas, Torres-Forné, Alejandro, Tsygankov, Sergey, İ Ünlütürk, Kıvanç, Valiante, Rosa, van de Meent, Maarten, Velhinho, José, Verbin, Yosef, Vercnocke, Bert, Vernieri, Daniele, Vicente, Rodrigo, Vitagliano, Vincenzo, Weltman, Amanda, Whiting, Bernard, Williamson, Andrew, Witek, Helvi, Wojnar, Aneta, Yakut, Kadri, Yan, Haopeng, Yazadjiev, Stoycho, Zaharijas, Gabrijela, Zilhão, Miguel, Barack, L, Cardoso, V, Nissanke, S, Sotiriou, T, Askar, A, Belczynski, C, Bertone, G, Bon, E, Blas, D, Brito, R, Bulik, T, Burrage, C, Byrnes, C, Caprini, C, Chernyakova, M, Chruściel, P, Colpi, M, Ferrari, V, Gaggero, D, Gair, J, García-Bellido, J, Hassan, S, Heisenberg, L, Hendry, M, Heng, I, Herdeiro, C, Hinderer, T, Horesh, A, Kavanagh, B, Kocsis, B, Kramer, M, Le Tiec, A, Mingarelli, C, Nardini, G, Nelemans, G, Palenzuela, C, Pani, P, Perego, A, Porter, E, Rossi, E, Schmidt, P, Sesana, A, Sperhake, U, Stamerra, A, Stein, L, Tamanini, N, Tauris, T, Urena-López, L, Vincent, F, Volonteri, M, Wardell, B, Wex, N, Yagi, K, Abdelsalhin, T, Aloy, M, Amaro-Seoane, P, Annulli, L, Arca-Sedda, M, Bah, I, Barausse, E, Barakovic, E, Benkel, R, Bennett, C, Bernard, L, Bernuzzi, S, Berry, C, Berti, E, Bezares, M, Blanco-Pillado, J, Blázquez-Salcedo, J, Bonetti, M, Bošković, M, Bosnjak, Z, Bricman, K, Brügmann, B, Capelo, P, Carloni, S, Cerdá-Durán, P, Charmousis, C, Chaty, S, Clerici, A, Coates, A, Colleoni, M, Collodel, L, Compère, G, Cook, W, Cordero-Carrión, I, Correia, M, de la Cruz-Dombriz, Á, Czinner, V, Destounis, K, Dialektopoulos, K, Doneva, D, Dotti, M, Drew, A, Eckner, C, Edholm, J, Emparan, R, Erdem, R, Ferreira, M, Ferreira, P, Finch, A, Font, J, Franchini, N, Fransen, K, Gal’Tsov, D, Ganguly, A, Gerosa, D, Glampedakis, K, Gomboc, A, Goobar, A, Gualtieri, L, Guendelman, E, Haardt, F, Harmark, T, Hejda, F, Hertog, T, Hopper, S, Husa, S, Ihanec, N, Ikeda, T, Jaodand, A, Jetzer, P, Jimenez-Forteza, X, Kamionkowski, M, Kaplan, D, Kazantzidis, S, Kimura, M, Kobayashi, S, Kokkotas, K, Krolik, J, Kunz, J, Lämmerzahl, C, Lasky, P, Lemos, J, Levi Said, J, Liberati, S, Lopes, J, Luna, R, Ma, Y, Maggio, E, Mangiagli, A, Montero, M, Maselli, A, Mayer, L, Mazumdar, A, Messenger, C, Ménard, B, Minamitsuji, M, Moore, C, Mota, D, Nampalliwar, S, Nerozzi, A, Nichols, D, Nissimov, E, Obergaulinger, M, Obers, N, Oliveri, R, Pappas, G, Pasic, V, Peiris, H, Petrushevska, T, Pollney, D, Pratten, G, Rakic, N, Racz, I, Radia, M, Ramazanoğlu, F, Ramos-Buades, A, Raposo, G, Rogatko, M, Rosca-Mead, R, Rosinska, D, Rosswog, S, Ruiz-Morales, E, Sakellariadou, M, Sanchis-Gual, N, Sharan Salafia, O, Samajdar, A, Sintes, A, Smole, M, Sopuerta, C, Souza-Lima, R, Stalevski, M, Stergioulas, N, Stevens, C, Tamfal, T, Torres-Forné, A, Tsygankov, S, İ Ünlütürk, K, Valiante, R, van de Meent, M, Velhinho, J, Verbin, Y, Vercnocke, B, Vernieri, D, Vicente, R, Vitagliano, V, Weltman, A, Whiting, B, Williamson, A, Witek, H, Wojnar, A, Yakut, K, Yan, H, Yazadjiev, S, Zaharijas, G, Zilhão, M, Barack, Leor, Cardoso, Vitor, Nissanke, Samaya, Sotiriou, Thomas P, Askar, Abbas, Belczynski, Chris, Bertone, Gianfranco, Bon, Edi, Blas, Diego, Brito, Richard, Bulik, Tomasz, Burrage, Clare, Byrnes, Christian T, Caprini, Chiara, Chernyakova, Masha, Chruściel, Piotr, Colpi, Monica, Ferrari, Valeria, Gaggero, Daniele, Gair, Jonathan, García-Bellido, Juan, Hassan, S F, Heisenberg, Lavinia, Hendry, Martin, Heng, Ik Siong, Herdeiro, Carlos, Hinderer, Tanja, Horesh, Assaf, Kavanagh, Bradley J, Kocsis, Bence, Kramer, Michael, Le Tiec, Alexandre, Mingarelli, Chiara, Nardini, Germano, Nelemans, Gijs, Palenzuela, Carlos, Pani, Paolo, Perego, Albino, Porter, Edward K, Rossi, Elena M, Schmidt, Patricia, Sesana, Alberto, Sperhake, Ulrich, Stamerra, Antonio, Stein, Leo C, Tamanini, Nicola, Tauris, Thomas M, Urena-López, L Arturo, Vincent, Frederic, Volonteri, Marta, Wardell, Barry, Wex, Norbert, Yagi, Kent, Abdelsalhin, Tiziano, Aloy, Miguel Ángel, Amaro-Seoane, Pau, Annulli, Lorenzo, Arca-Sedda, Manuel, Bah, Ibrahima, Barausse, Enrico, Barakovic, Elvis, Benkel, Robert, Bennett, Charles L, Bernard, Laura, Bernuzzi, Sebastiano, Berry, Christopher P L, Berti, Emanuele, Bezares, Miguel, Blanco-Pillado, Jose Juan, Blázquez-Salcedo, Jose Luis, Bonetti, Matteo, Bošković, Mateja, Bosnjak, Zeljka, Bricman, Katja, Brügmann, Bernd, Capelo, Pedro R, Carloni, Sante, Cerdá-Durán, Pablo, Charmousis, Christos, Chaty, Sylvain, Clerici, Aurora, Coates, Andrew, Colleoni, Marta, Collodel, Lucas G, Compère, Geoffrey, Cook, William, Cordero-Carrión, Isabel, Correia, Miguel, de la Cruz-Dombriz, Álvaro, Czinner, Viktor G, Destounis, Kyriakos, Dialektopoulos, Kostas, Doneva, Daniela, Dotti, Massimo, Drew, Amelia, Eckner, Christopher, Edholm, James, Emparan, Roberto, Erdem, Recai, Ferreira, Miguel, Ferreira, Pedro G, Finch, Andrew, Font, Jose A, Franchini, Nicola, Fransen, Kwinten, Gal’tsov, Dmitry, Ganguly, Apratim, Gerosa, Davide, Glampedakis, Kostas, Gomboc, Andreja, Goobar, Ariel, Gualtieri, Leonardo, Guendelman, Eduardo, Haardt, Francesco, Harmark, Troels, Hejda, Filip, Hertog, Thomas, Hopper, Seth, Husa, Sascha, Ihanec, Nada, Ikeda, Taishi, Jaodand, Amruta, Jetzer, Philippe, Jimenez-Forteza, Xisco, Kamionkowski, Marc, Kaplan, David E, Kazantzidis, Stelios, Kimura, Masashi, Kobayashi, Shiho, Kokkotas, Kostas, Krolik, Julian, Kunz, Jutta, Lämmerzahl, Claus, Lasky, Paul, Lemos, José P S, Levi Said, Jackson, Liberati, Stefano, Lopes, Jorge, Luna, Raimon, Ma, Yin-Zhe, Maggio, Elisa, Mangiagli, Alberto, Montero, Marina Martinez, Maselli, Andrea, Mayer, Lucio, Mazumdar, Anupam, Messenger, Christopher, Ménard, Brice, Minamitsuji, Masato, Moore, Christopher J, Mota, David, Nampalliwar, Sourabh, Nerozzi, Andrea, Nichols, David, Nissimov, Emil, Obergaulinger, Martin, Obers, Niels A, Oliveri, Roberto, Pappas, George, Pasic, Vedad, Peiris, Hiranya, Petrushevska, Tanja, Pollney, Denis, Pratten, Geraint, Rakic, Nemanja, Racz, Istvan, Radia, Miren, Ramazanoğlu, Fethi M, Ramos-Buades, Antoni, Raposo, Guilherme, Rogatko, Marek, Rosca-Mead, Roxana, Rosinska, Dorota, Rosswog, Stephan, Ruiz-Morales, Ester, Sakellariadou, Mairi, Sanchis-Gual, Nicolás, Sharan Salafia, Om, Samajdar, Anuradha, Sintes, Alicia, Smole, Majda, Sopuerta, Carlos, Souza-Lima, Rafael, Stalevski, Marko, Stergioulas, Nikolaos, Stevens, Chris, Tamfal, Tomas, Torres-Forné, Alejandro, Tsygankov, Sergey, İ Ünlütürk, Kıvanç, Valiante, Rosa, van de Meent, Maarten, Velhinho, José, Verbin, Yosef, Vercnocke, Bert, Vernieri, Daniele, Vicente, Rodrigo, Vitagliano, Vincenzo, Weltman, Amanda, Whiting, Bernard, Williamson, Andrew, Witek, Helvi, Wojnar, Aneta, Yakut, Kadri, Yan, Haopeng, Yazadjiev, Stoycho, Zaharijas, Gabrijela, and Zilhão, Miguel
Abstract: The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.
Published: 2019

31. Topics of Measure Theory on Infinite Dimensional Spaces

Author: Velhinho, José and uBibliorum
Subjects: infinite dimensional space, projective limit, General Mathematics, Gaussian, nuclear space, measure, Nuclear space, Space (mathematics), Measure (mathematics), Finite-dimensional distribution, symbols.namesake, Computer Science (miscellaneous), Engineering (miscellaneous), Infinite dimensional space, Mathematics, Discrete mathematics, lcsh:Mathematics, Projective limit, lcsh:QA1-939, Measure, Algebra, Transformation (function), Product (mathematics), symbols, Product measure
Abstract: Submitted by VELHINHO (jvelhi@ubi.pt) on 2019-10-11T13:42:05Z No. of bitstreams: 1 Mathematics_05-00044.pdf: 490628 bytes, checksum: 3d1c18a8de835a426dc6191f92a42923 (MD5) Approved for entry into archive by Pessoa (pfep@ubi.pt) on 2019-10-11T13:56:46Z (GMT) No. of bitstreams: 1 Mathematics_05-00044.pdf: 490628 bytes, checksum: 3d1c18a8de835a426dc6191f92a42923 (MD5) Approved for entry into archive by Pessoa (pfep@ubi.pt) on 2019-10-11T14:00:10Z (GMT) No. of bitstreams: 1 Mathematics_05-00044.pdf: 490628 bytes, checksum: 3d1c18a8de835a426dc6191f92a42923 (MD5) Made available in DSpace on 2019-10-11T14:00:11Z (GMT). No. of bitstreams: 1 Mathematics_05-00044.pdf: 490628 bytes, checksum: 3d1c18a8de835a426dc6191f92a42923 (MD5) Previous issue date: 2017-08-29 info:eu-repo/semantics/publishedVersion
Published: 2017

32. Unitary dynamics as a uniqueness criterion for the quantization of Dirac fields

Author: Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Subjects: Physics::History of Physics
Abstract: Friedrich-Alexander-Universität, Erlangen-Nürnberg, July 26, 2017. -- https://www.gravity.physik.fau.de/calendar/unitary-dynamics-as-a-uniqueness-criterion-for-the-quantization-of-dirac-fields/, It is well known that linear canonical transformations are not generally implemented as unitary operators in QFT. Such transformations include the dynamics that arises from linear field equations on the background spacetime. This evolution is specially relevant in nonstationary backgrounds, where there is no time-translational symmetry that can be exploited to select a quantum theory. We investigate whether it is possible to find a Fock representation for the canonical anticommutation relations of a Dirac field, propagating on homogeneous and isotropic cosmological backgrounds, on the one hand, and on tridimensional conformally ultrastatic spacetimes, on the other hand, such that the field evolution is unitarily implementable. First, we restrict our attention to Fock representations that are invariant under the group of symmetries of the system. Then, we prove that there indeed exist Fock representations such that the dynamics is implementable as a unitary operator. Finally, once a convention for the notion of particles and antiparticles is set, we show that these representations are all unitarily equivalent.
Published: 2017

33. Fock quantization of the Dirac field in cosmology with unitary dynamics

Author: Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Velhinho, José M., Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Published: 2018

34. On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology

Author: Cortez, Jerónimo, primary, Inácio Rodrigues, Ilda, additional, Martín-Benito, Mercedes, additional, and Velhinho, José, additional
Published: 2018
Full Text: View/download PDF

35. Man on the moon: The case for unitary dynamics

Author: Mena Marugán, Guillermo A., Cortez, Jerónimo, and Velhinho, José M.
Subjects: General Relativity and Quantum Cosmology
Abstract: Presentación de 26 págs.; Eigth Jerte Advanced Relativity and Related Analogs in Matter Physics, Loop Approaches and Symmetries; Navaconcejo, Cáceres (España); 23-26 de mayo de 2016, Quantum field theory is plagued with ambiguities, even for the Fock quantization of linear fields. There are infinite non-equivalent Fock representations of the Weyl algebra for fields. In stationary or highly symmetric spacetimes, there exist uniqueness criteria for the choice of a (unitary class of) representation(s). Recently, a criterion has been suggested to attain uniqueness also in non-stationary backgrounds, like in cosmological spacetimes The criterion is the vacuum invariance under the symmetries of the field equations, together with the unitary implementability of the dynamics. This criterion picks out a privileged parametrization of the field canonical pair, including rescalings, and fixes a family of unitarily equivalent representations for this pair. It has been successfully applied in FLRW and in Gowdy (anisotropic) spacetimes, for scalar fields and for fermions. Alternatively, a generalized notion of unitarity has been proposed to alleviate the tension that only one field parametrization admits a unitary evolution. We explain why, in our opinion, this tension is artifici
Published: 2016

36. Unique quantization of a Dirac field with unitary dynamics

Author: Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: Presentación con 42 diapositivas ; Fourth Tux Workshop on Quantum Gravity, Tux, Austria, February 15-19, 2016
Published: 2016

37. The Dirac fermion in cosmology: uniqueness criteria

Author: Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: Conferencia invitada ; Navaconcejo, Cáceres (España); 23-26 de mayo de 2016
Published: 2016

38. Convertible Subspaces of Hessenberg-Type Matrices

Author: da Cruz, Henrique, primary, Rodrigues, Ilda, additional, Serôdio, Rogério, additional, Simões, Alberto, additional, and Velhinho, José, additional
Published: 2017
Full Text: View/download PDF

39. Topics of Measure Theory on Infinite Dimensional Spaces

Author: Velhinho, José, primary
Published: 2017
Full Text: View/download PDF

40. Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

Author: Cortez, Jerónimo, primary, Navascués, Beatriz Elizaga, additional, Martín-Benito, Mercedes, additional, Mena Marugán, Guillermo A., additional, and Velhinho, José M., additional
Published: 2017
Full Text: View/download PDF

41. Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

Author: Fundação para a Ciência e a Tecnologia (Portugal), Netherlands Organization for International Cooperation in Higher Education, European Cooperation in Science and Technology, Universidad Nacional Autónoma de México, Ministerio de Economía y Competitividad (España), Consejo Nacional de Ciencia y Tecnología (México), Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Velhinho, José M., Fundação para a Ciência e a Tecnologia (Portugal), Netherlands Organization for International Cooperation in Higher Education, European Cooperation in Science and Technology, Universidad Nacional Autónoma de México, Ministerio de Economía y Competitividad (España), Consejo Nacional de Ciencia y Tecnología (México), Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in nonstationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable nontrivial quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obtains an essentially unique splitting of the time variation of the Dirac field into an explicit dependence on the background scale factor and a quantum evolution of the corresponding creation and annihilation operators.
Published: 2017

42. Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

Author: Cortez, Jerónimo, primary, Elizaga Navascués, Beatriz, additional, Martín-Benito, Mercedes, additional, Mena Marugán, Guillermo A., additional, and Velhinho, José M., additional
Published: 2017
Full Text: View/download PDF

43. Uniqueness of the Fock quantization of Dirac fields with unitary dynamics

Author: Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Velhinho, José M., Elizaga Navascués, Beatriz, Cortez, Jerónimo, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Published: 2016

44. Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

Author: Consejo Nacional de Ciencia y Tecnología (México), Universidad Nacional Autónoma de México, Netherlands Organization for Scientific Research, Ministerio de Economía y Competitividad (España), Radboud University, European Cooperation in Science and Technology, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Velhinho, José M., Consejo Nacional de Ciencia y Tecnología (México), Universidad Nacional Autónoma de México, Netherlands Organization for Scientific Research, Ministerio de Economía y Competitividad (España), Radboud University, European Cooperation in Science and Technology, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
Published: 2016

45. Uniqueness of the Fock quantization of scalar fields in a Bianchi i cosmology with unitary dynamics

Author: Programa de Desarrollo de las Ciencias Básicas (Uruguay), National Science Foundation (US), Netherlands Organization for Scientific Research, Consejo Nacional de Ciencia y Tecnología (México), Universidad Nacional Autónoma de México, Ministerio de Economía y Competitividad (España), European Cooperation in Science and Technology, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Olmedo, Javier, Velhinho, José M., Programa de Desarrollo de las Ciencias Básicas (Uruguay), National Science Foundation (US), Netherlands Organization for Scientific Research, Consejo Nacional de Ciencia y Tecnología (México), Universidad Nacional Autónoma de México, Ministerio de Economía y Competitividad (España), European Cooperation in Science and Technology, Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Olmedo, Javier, and Velhinho, José M.
Abstract: The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, a choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology. © 2016 American Physical Society
Published: 2016

46. Unique Fock quantization of a massive fermion field in a cosmological scenario

Author: Universidad Nacional Autónoma de México, Consejo Nacional de Ciencia y Tecnología (México), European Cooperation in Science and Technology, Netherlands Organization for Scientific Research, Ministerio de Economía y Competitividad (España), Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., Velhinho, José M., Universidad Nacional Autónoma de México, Consejo Nacional de Ciencia y Tecnología (México), European Cooperation in Science and Technology, Netherlands Organization for Scientific Research, Ministerio de Economía y Competitividad (España), Cortez, Jerónimo, Elizaga Navascués, Beatriz, Martín-Benito, Mercedes, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive at this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a nontrivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set. © 2016 American Physical Society
Published: 2016

47. Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics

Author: Cortez, Jerónimo, primary, Navascués, Beatriz Elizaga, additional, Martín-Benito, Mercedes, additional, Mena Marugán, Guillermo A., additional, Olmedo, Javier, additional, and Velhinho, José M., additional
Published: 2016
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48. Unique Fock quantization of a massive fermion field in a cosmological scenario

Author: Cortez, Jerónimo, primary, Elizaga Navascués, Beatriz, additional, Martín-Benito, Mercedes, additional, Mena Marugán, Guillermo A., additional, and Velhinho, José M., additional
Published: 2016
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49. Quantum unitary dynamics in cosmological spacetimes

Author: Ministerio de Ciencia e Innovación (España), Ministerio de Economía y Competitividad (España), Consejo Nacional de Ciencia y Tecnología (México), European Cooperation in Science and Technology, Cortez, Jerónimo, Mena Marugán, Guillermo A., Velhinho, José M., Ministerio de Ciencia e Innovación (España), Ministerio de Economía y Competitividad (España), Consejo Nacional de Ciencia y Tecnología (México), European Cooperation in Science and Technology, Cortez, Jerónimo, Mena Marugán, Guillermo A., and Velhinho, José M.
Abstract: © 2015 Elsevier Inc. We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Published: 2015

50. Unitary evolution as a uniqueness criterion

Author: Cortez, Jerónimo, Mena Marugán, Guillermo A., Olmedo, Javier, Velhinho, José M., Cortez, Jerónimo, Mena Marugán, Guillermo A., Olmedo, Javier, and Velhinho, José M.
Abstract: It is well known that the process of quantizing field theories is plagued with ambiguities. First, there is ambiguity in the choice of basic variables describing the system. Second, once a choice of field variables has been made, there is ambiguity concerning the selection of a quantum representation of the corresponding canonical commutation relations. The natural strategy to remove these ambiguities is to demand positivity of energy and to invoke symmetries, namely by requiring that classical symmetries become unitarily implemented in the quantum realm. The success of this strategy depends, however, on the existence of a sufficiently large group of symmetries, usually including time-translation invariance. These criteria are therefore generally insufficient in non-stationary situations, as is typical for free fields in curved spacetimes. Recently, the criterion of unitary implementation of the dynamics has been proposed in order to select a unique quantization in the context of manifestly non-stationary systems. Specifically, the unitarity criterion, together with the requirement of invariance under spatial symmetries, has been successfully employed to remove the ambiguities in the quantization of linearly polarized Gowdy models as well as in the quantization of a scalar field with time varying mass, propagating in a static background whose spatial topology is either of a d-sphere (with d = 1, 2, 3) or a three torus. Following Ref. 3, we will see here that the symmetry and unitarity criteria allows for a complete removal of the ambiguities in the quantization of scalar fields propagating in static spacetimes with compact spatial sections, obeying field equations with an explicitly time-dependent mass, of the form These results apply in particular to free fields in spacetimes which, like e.g. in the closed FRW models, are conformal to a static spacetime, by means of an exclusively time-dependent conformal factor. In fact, in such cases the free field equation can b
Published: 2015

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