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International audience; Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A≈120 nuclei is reported for the first time. One of the four reported bands in 119Cs, built on a 11/2− state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled πh11/2[505]11/2− configuration associated with oblate shape. Together with the decoupled πh11/2[541]3/2− band built on the 11/2− prolate state at 110 keV, for which a half-life of T1/2=55(5)μs has been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A≈120 nuclei, a phenomenon predicted since long time, but not yet observed. Calculations using the particle-number conserving cranked shell model and two dimensional tilted axis cranking covariant density functional theory support and well reproduce the observed oblate and prolate coexisting low-energy states in 119Cs.

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

In this study we present a universal effective action for one-loop matching of all scalar leptoquarks. We use both the Universal One-Loop Effective Action (UOLEA) and covariant diagrams to evaluate the Wilson coefficients directly in the Green basis for up-to dimension-6 operators. On the technical side, we use the newly developed method of evaluating supertraces, to further validate the results stemming from the use of covariant diagrams. As an application, we perform a fully functional matching onto Standard Model Effective Field Theory (SMEFT) of a model with two scalar leptoquark fields: a weak isospin singlet and a doublet. We demonstrate its use by calculating several observables, such as lepton magnetic and electric dipole moments, neutrino masses, proton decay rate, while we comment upon fine tuning issues in this model. Apart from its phenomenological interest, this model generates the majority of dimension-6 operators and provides an EFT benchmark towards future matching automation., Comment: 69 pages, v2: references added, v3: few sign errors and typos corrected, refs added, version matches JHEP publication

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

We carry out the canonical analysis of a covariant version of unimodular gravity in terms of the connection representation. We then proceed to quantize this theory by implementing the Dirac procedure. We confirm whether and how the Kodama state, which is a solution of quantum general relativity, can be extended into covariant unimodular gravity. Finally, we discuss the difference of quantum states between covariant unimodular gravity, the original unimodular gravity, and general relativity., 9 pages

The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of Maxwell's electrodynamics arises in the flat Minkowski spacetime when the general coordinate transformations are restricted to a class of transformations preserving the Minkowski line element. The particular attention is paid to the analysis of the electromagnetism in the noninertial rotating reference system. For the latter case, the general stationary solution of the Maxwell equations in the absence of the electric current is constructed in terms of the two scalar functions satisfying the Poisson and the biharmonic equations with an arbitrary charge density as a matter source. The classic problem of Schiff is critically revisited., Comment: 24 pages, Revtex, no figures, to appear in European Physical Journal C

Classical isomorphism theorems due to Dynkin, Eisenbaum, Le Jan, and Sznitman establish equalities between the correlation functions or distributions of occupation times of random paths or ensembles of paths and Markovian fields, such as the discrete Gaussian free field. We extend these results to the case of real, complex, or quaternionic vector bundles of arbitrary rank over graphs endowed with a connection, by providing distributional identities between functionals of the Gaussian free vector field and holonomies of random paths. As an application, we give a formula for computing moments of a large class of random, in general non-Gaussian, fields in terms of holonomies of random paths with respect to an annealed random gauge field, in the spirit of Symanzik's foundational work on the subject., Comment: 51 pages, 10 figures. This version contains a new introduction, an additional Section (6.8) detailing an important example (the case of trace-positive holonomies), and a treatment of the quaternionic case. The introductory material on continuous time random walks on multigraphs in Section 1 was also simplified

This work presents a first full one-loop computation of vector boson scattering (VBS) within the non-linear effective field theory given by the bosonic sector of the usually called electroweak chiral Lagrangian (EChL). The computation is performed in the most general case of covariant Rξ gauges and is compared through all this work with the Standard Model case, whose computation in these covariant gauges is also novel and is presented also here. The calculation of the one-loop VBS amplitude is performed using the diagrammatic method by means of the one-particle-irreducible (1PI) Green functions that are involved in these scattering processes. The central part of this work is then devoted to the renormalization of all the n-legs one-loop 1PI Green functions involved. This renormalization is performed in the most general off-shell case with arbitrary external legs momenta. We then describe in full detail the renormalization program, which within this context of the EChL, implies to derive all the counterterms for both the electroweak parameters, like boson masses and gauge couplings, and those for the EChL coefficients. These later are crucial for the renormalization of the new divergences typically appearing when computing loops with the lowest chiral dimension Lagrangian. We present here the full list of involved divergences and counterterms in the Rξ gauges and derive the complete set of renormalization group equations for the EChL coefficients. In the last part of this work, we present the EChL numerical results for the one-loop cross section in the WZ channel and compare them with the SM results.

When a simply connected domain D ⊂ Rd (d ≥ 2) is approximated in a “good” way by embedded connected weighted graphs, we prove that the transfer current matrix (defined on the edges of the graph viewed as an electrical network) converges, up to a local weight factor, to the differential of Green’s function on D. This observation implies that properly rescaled correlations of the spanning tree model and correlations of minimal subconfigurations in the abelian sandpile model have a universal and conformally covariant limit. We further show that, on a periodic approximation of the domain, all pattern fields of the spanning tree model, as well as the minimal-pattern (e.g. zero-height) fields of the sandpile, converge weakly in distribution to Gaussian white noise., Probability Theory and Related Fields, 163 (1), ISSN:0178-8051, ISSN:1432-2064

Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of ‘scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to ‘move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times, (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.

It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in arXiv:2008.09387. In this paper, we start to extend this analysis to the quantum realm. We identify two types of covariant singularities in field space corresponding to geodesic incompleteness and ill-defined path integrals (hereby dubbed functional singularities). We argue that the former might not be harmful after all, whilst the latter makes all observables undefined. We show that the path-integral measure is regular in any four-dimensional theory of gravity without matter or in any theory in which gravity is either absent or treated semi-classically. This might suggest the absence of functional singularities in these cases, however it can only be confirmed with a thorough analysis, case by case, of the path integral. We provide a topological and model-independent classification of functional singularities using homotopy groups and we discuss examples of theories with and without such singularities., Comment: Accepted for publication in Nucl. Phys. B

Kitaev's lattice models are usually defined as representations of the Drinfeld quantum double $D(H)=H\bowtie H^{*\text{op}} $, as an example of a double cross product quantum group. We propose a new version based instead on $M(H)=H^{\text{cop}}\blacktriangleright\!\!\!\triangleleft H$ as an example of Majid's bicrossproduct quantum group, related by semidualisation or `quantum Born reciprocity' to $D(H)$. Given a finite-dimensional Hopf algebra $H$, we show that a quadrangulated oriented surface defines a representation of the bicrossproduct quantum group $H^{\text{cop}}\blacktriangleright\!\!\!\triangleleft H$. Even though the bicrossproduct has a more complicated and entangled coproduct, the construction of this new model is relatively natural as it relies on the use of the covariant Hopf algebra actions. Working locally, we obtain an exactly solvable Hamiltonian for the model and provide a definition of the ground state in terms of a tensor network representation., 34 pages

We use a covariant formalism that is capable of describing the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. By considering that only local interactions of a quantum particle with the quantum field can affect its behavior, we show that the magnetic Aharonov-Bohm effect must be present even if the solenoid generating the magnetic field is shielded by a perfect conductor, as experimentally demonstrated., 5 pages, 1 figure. V2: The new version is focused on the Aharonov-Bohm and Aharonov-Casher effects, without general claims about quantum phases

A modified $GW$ approximation to many - body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects high order connected correlation functions. A covariant (preserving Ward identities due to charge conservation) scheme for two - body correlators is employed, which holds the relation between the charge correlator and charge susceptibility. The method is tested on the two - dimensional one - band Hubbard model. Results are compared with exact diagonalization, the fluctuation - exchange (FLEX) theory and determinantal quantum Monte Carlo (DQMC) approach. The comparison for the (one - body) Green's function demonstrates that it is more precise in strong - coupling regime (especially away from half - filling) than similar - complexity approximations $GW$ or FLEX. The charge correlator is in excellent agreement with the numerically exact result obtained from DQMC., Comment: 21 pages, 7 figures

We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner., Comment: 27 pages + Appendix, 2 figures; v3 published version

We develop a flexible, relativistically covariant parameterization of dense nuclear matter equation of state suited for inclusion in computationally demanding hadronic transport simulations. Within an implementation in the hadronic transport code SMASH, we show that effects due to bulk thermodynamic behavior are reproduced in dynamic hadronic systems, demonstrating that hadronic transport can be used to study critical behavior in dense nuclear matter, both at and away from equilibrium. We also show that two-particle correlations calculated from hadronic transport simulation data follow theoretical expectations based on the second order cumulant ratio, and constitute a clear signature of crossing the phase diagram above the critical point., 31 pages, 14 figures. Revised version to be published in PRC (in press). We added a discussion of correlations in hadronic transport and improved the proof of the relationship between the second order cumulant and the pair distribution function at close distances

In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for spacetime parameterization is presented and the equations defining Dirac spinors are written fully in terms of Lorentz scalars. After presenting how the tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate Lorentz structures, a covariant recipe for the calculation of scalar bilinears is provided., Comment: 10 pages, 1 figure

We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking., Comment: 48 pages; v2: added appendix A.3 with comments and comparisons with earlier work; v3: fixed references and typos

This short letter refers to Schmutzer’s 5-dimensional Projective Unified Field Theory as a new general-relativistic covariant unification of gravitation, electromagnetism and scalarism. The scalarism appearing in the theory is a new phenomenon of nature, which can be interpreted as dark matter. A number of applications to the orbits of spaceships, planets and stars in galaxies as well as to the cosmos as a whole generate new effects that go beyond the known statements of the Einstein-Maxwell theory.

We investigate how the comoving curvature and tensor perturbations are transformed under the generalized disformal transformation with the second-order covariant derivatives of the scalar field, where the free functions depend on the fundamental elements constructed with the covariant derivatives of the scalar field with at most the quadratic order of the second-order covariant derivatives. Our analysis reveals that on the superhorizon scales the difference between the comoving curvature perturbations in the original and new frames is given by the combination of the time derivative of the comoving curvature perturbation, the intrinsic entropy perturbation of the scalar field, and its time derivative in the original frame. Thus, in the case that on the superhorizon scales (1) the intrinsic entropy perturbation and its time derivative vanish and (2) the comoving curvature perturbation in the original frame, ${\cal R}_c$, is conserved, the comoving curvature perturbation becomes invariant under the disformal transformation on the superhorizon scales. We also show that the tensor perturbations are also disformally invariant, in the case that the tensor perturbations in the original frame are conserved with time., 11 pages, published version

Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature., 28 pages+refs

6 pags., We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological approach provided by the relative bicomplex framework. Finally, we discuss some of the physical implications derived from this equivalence in the context of singularity identification through curvature invariants., This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación FIS2017-84440-C2-2-P grant. J. M. B. is supported by the Eberly Research Funds of Penn State, by the NSF Grant No. PHY-1806356 and by the Urania Stott fund of Pittsburgh foundation No. UN2017-92945. E. J. S. V. is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O'Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group ${\rm SU}(2)$ and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton's constant., 38 pages + appendix + refs, 2 figures; v2 minor improvements, journal version

We construct a new covariant action for "flat" self-dual gravity in four spacetime dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure., Comment: 18 pages

The effective approach is applied to the analysis of inflationary magnetogenesis. Rather than assuming a particular underlying description, all the generally covariant terms potentially appearing with four space-time derivatives in the effective action have been included and weighted by inflaton-dependent couplings. The higher derivatives are suppressed by the negative powers of a typical mass scale whose specific values ultimately depend on the tensor to scalar ratio. During a quasi-de Sitter stage the corresponding corrections always lead to an asymmetry between the hypermagnetic and the hyperelectric susceptibilities. After presenting a general method for the estimate of the gauge power spectra, the obtained results are illustrated for generic models and also in the case of some non-generic scenarios where either the inflaton has some extra symmetry or the higher-order terms are potentially dominant., 10 pages, 2 figures

Using probability operators and Fourier transforms of CP-instruments on von Neumann algebras, we give necessary and sufficient conditions for operators to be probability operators associated with covariant CP-instruments or to be Fourier transforms of covariant CP-instruments. We discuss a convolution semigroup of covariant CP-instruments and a semigroup of probability operators associated with CP-instruments on von Neumann algebras.

We study the entropic destruction of heavy quarkonium in strongly coupled theories with an anisotropic scaling symmetry in time and spatial direction. We consider Lifshitz and hyperscaling violation theories which are covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent $z$ and hyperscaling violation exponent $\theta$. It is shown that the entropic force depends on the parameters of these theories. In particular, increasing $z$ decreases the entropic force thus reducing the quarkonium dissociation, while increasing $\theta$ has opposite effect., Comment: 7 pages, 3 figures, to be published in Chinese Physics C

We consider the cosmology obtained using scalar fields with a negative potential energy, such as employed to obtain an Ekpyrotic phase of contraction. Applying the covariant entropy bound to the tower of states dictated by the distance conjecture, we find that the relative slope of the potential $|V^{\prime}| / |V|$ is bounded from below by a constant of the order one in Planck units. This is consistent with the requirement to obtain slow Ekpyrotic contraction. We also derive a refined condition on the potential which holds near local minima of a negative potential., Comment: 8 pages, 2 figures; v2: 14 pages, 2 figures; references and comments on conformal diagrams added; matches published version

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $\mathcal{U}_{\theta }(su(2,2)\ltimes T^{4}$) and $\mathcal{U}_{\bar{\theta}}(su(2,2)\ltimes\bar{T}^{4}$), where $T^{4}$ describe complex twistor coordinatesand $\bar{T}^{4}$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (HCA) $su(2,2)\ltimes H^{4,4}_\hslash$ ($H^{4,4}_\hslash=\bar{T}^4 \ltimes_\hslash T_4$ is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length $\lambda_p$ will be called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We shall describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and by the quantization map in $H_\hslash^{4,4}$. We introduce as well generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra $\mathcal{U}_\theta(su(2,2)\ltimes T^4).$, Comment: 23 pages; Dedicated on 90-th Birthday to Sir Roger Penrose as a tribute to his ideas and achievements,{Submitted to Special Issue of SYMMETRY "Quantum Group Symmetry and Quanatum Geometry", ed. A. Ballesteros, G. Gubitosi, F.J. Herranz (2021)}; v2-as published on 15.07.2021 in SYMMETRY

Weyl particles exhibit chiral transport property under external curved space-time geometry. This effect is called the chiral gravitational effect, which plays an important role in quantum field theory. However, the absence of real Weyl particles in nature hinders the observation of such interesting phenomena. In this paper, we show that chiral gravitational effect can be manifested in Weyl metamaterials with spatially controlled nonlocality. This inhomogeneous modulation results in a spatially dependent group velocity in the Weyl cone dispersion, which is equivalent to introducing a curved background space-time (or gravitational field) for Weyl pseudospinors according to the Clifford algebra. The Weyl equation describing the Weyl cone dispersions is reformulated into the covariant form that contains a nonAbelian gauge field by considering the parallel transport of pseudospinors. The synthetic gravitational field (i.e., space-time curvature) leads to the quantization of energy levels, including chiral zeroth order energy modes (or simply chiral zero modes) that determine the chiral transport property of pseudospinors. Inhomogeneous Weyl metamaterials can potentially become a platform for investigating the interaction between Weyl particles and gravitational fields in future table-top experiments. The theoretical model and the associated results may serve as a guidance for experimentalists to observe such chiral transport effects in photonic Weyl systems.

We introduce, within the Refined-Gribov-Zwanziger setup, a composite BRST invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behaviour of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure., 31 pages. Some remarks were added

We study canonical and affine versions of the quantized covariant Euclidean Higgs scalar field-theory for two real fields on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume., 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:2103.06746

The object of this article is to introduce a covariant description for a thermo-mechanical continuum. The conservation equations are written in this context and a constitutive model is derived for a reversible transformation. It is then possible to formulate a weak form of the problem to be solved for the finite transformations of a solid. A finite-element computation is next proposed using this approach for thermo-mechanical problems. The advantages of such a formulation are highlighted throughout the article.

Refining a theorem of Zarhin, we prove that given a $g$-dimensional abelian variety $X$ and an endomorphism $u$ of $X$, there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z})$ such that each Tate module $T_\ell X$ has a $\mathbb{Z}_\ell$-basis on which the action of $u$ is given by $A$., 3 pages

Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature., arXiv admin note: text overlap with arXiv:1911.01907 Correcting typos. We added a few comments and the diagrammatic representation of the Feynman rules, according to the referee's requests

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model., Version as published on Phys. Rev. D

In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers-Perry spacetime with equal momenta and the scalar field is identified with the Hamilton-Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers-Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers-Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity-1 character of the Myers-Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity-1 metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr-(A)dS case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory., Comment: 19 pages (added new references)

Recent works have explored non-perturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a non-trivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Inhere, we restore the BRST symmetry which is softly broken by the elimination of gauge copies and provide a BRST-invariant discussion of such a transition. In order to make clear all physical statements, we deal with linear covariant gauges which contain a gauge parameter and therefore allow for an explicit check of gauge parameter independence of physical results. We also discuss the generation of condensates due to the infrared relevance of infinitesimal Gribov copies., 11 pages, no figures

An efficient algorithm is developed for compactly weaving all the Lorentz covariant three-point vertices in relation to the decay of a massive particle $X$ of mass $m_X$ and spin $J$ into two particles $ M_{1,2}$ with equal mass $m$ and spin $s$. The closely-related equivalence between the helicity formalism and the covariant formulation is utilized so as to identify the basic building blocks for constructing the covariant three-point vertex corresponding to each helicity combination explicitly. The massless case with $m=0$ is worked out straightforwardly and the (anti)symmetrization of the three-point vertex required by spin statistics of identical particles is made systematically. It is shown that the off-shell electromagnetic photon coupling to the states $M_1$ and $M_2$ can be accommodated in this framework. The power of the algorithm is demonstrated with a few typical examples with specific $J$ and $s$ values., 18 pages, 5 figures

The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time relativistic formalism of single-particle operators. Starting from the premise that physical variables associated with the proper-time gauge have a prominent role in the specification of position, since they do not depend on classical parameters connected to an external observer, we obtain a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper time. Among the consequences of this result, we emphasize that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.

It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general covariance. Here, however, we show that a dedicated space-time analysis is still required, even in the case of a bijective canonical transformation. In addition, a complete global analysis is presented for a recent proposal of a non-bijective transformation, showing that it does not preserve general covariance and that the only novel physical effect introduced by the modification is the presence of certain time-reversal hypersurfaces between classical space-time regions. These results provide further insights into the physical interpretation of modified dynamics in models of loop quantum gravity., 15 pages, v2: new extended example of a bijective canonical transformation

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation., Comment: 21 pages, 11 figures, 3 tables

We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a scalar to a matrix quantity. Reparametrization invariance along the rays allows a covariant formulation where propagation can take place along a general curve. A general gradient index background is used to demonstrate the scheme. This affords a description of classical imaging optics when the polarization aspects may be varying rapidly and cannot be neglected., 10 pages, 4 figures, minor changes and references included

International audience; The Fourier modal method (FMM) is certainly one of the most popular and general methods for the modeling of diffraction gratings. However for non-lamellar gratings it is associated with a staircase approximation of the profile leading to poor convergence rate for metallic gratings in TM polarization. One way to overcome the above weakness of the FMM is the use of the fast Fourier factorization (FFF) first derived for the differential method. That approach relies on the definition of normal and tangential vectors to the profile. Instead, we introduce a coordinate system that matches laterally the profile and solve the covariant Maxwell's equations in the new coordinate system, hence the name matched coordinate method (MCM). Comparison of efficiencies computed with MCM with other data from the literature validates the method.

We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of $C^*$-correspondences. This extends a recent Wold-type decomposition by Jeu and Pinto for a $q$-doubly commuting isometries. Application to the wandering subspaces of doubly commuting induced representations is explored, and a version of Mandrekar's Beurling type theorem is obtained to study doubly commuting invariant subspaces using Fock space approach due to Popescu., Comment: 26pages, revised version

We report on the improvement of our isobar models for elementary kaon photo- and electroproduction, $$\gamma _\mathrm{r,v}+N\rightarrow K+Y$$ , during the last two decades. Our effort started with the investigation of kaon photoproduction near threshold, followed by the construction of new models which were intended to explain all $$K\Lambda $$ and $$K\Sigma $$ data from threshold up to $$W\approx 3$$ GeV by using two approaches, i.e., the partial waves and the fully covariant isobar models. Both approaches yield nice agreement with the presently available experimental data. A number of applications of the models in nuclear and particle physics area are presented. We also discuss our effort to use the pure spin-3/2 and spin-5/2 propagators in meson scattering and meson photoproduction processes.

We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple presentation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order $\epsilon$-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators., Comment: 134 pages, 8 figures

We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number $l \geq 2$, while for low multipole modes with $l$ $=$ $0$ or $1$ -- for which Regge-Wheeler gauge is inapplicable -- we propose a set of gauge fixing conditions which are 2D background covariant and perturbatively well-defined. We find that the corresponding Faddeev-Popov ghosts are non-propagating for the $l\geq2$ modes, but are in general nontrivial for the low multipole modes with $l = 0,1$. However, in Schwarzschild coordinates, all time derivatives acting on the ghosts drop from the action and the low multipole ghosts have instantaneous propagators. Up to possible subtleties related to quantizing gravity in a space with a horizon, Faddeev's theorem suggests the possibility of an underlying canonical (Hamiltonian) quantization with a manifestly ghost-free Hilbert space., 29 p

We derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of Lax connections of Zakharov-Shabat type, which includes an ultralocal variant of the principal chiral model as a special case. At the $2$d level, we determine for the first time the covariant Poisson bracket $r$-matrix structure of the Zakharov-Shabat Lax connection, which is of rational type. The flatness condition is then derived as a covariant Hamilton equation. We obtain a remarkable formula for the covariant Hamiltonian in term of the Lax connection which is the covariant analogue of the well-known formula "$H=Tr L^2$"., 16 pages. Final authors' version with added references and explanations

Journal of high energy physics 06(6), 012 (2021). doi:10.1007/JHEP06(2021)012, Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to ${\cal O}(G^2)$, which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins., Published by SISSA, [Trieste]