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Combining quantum theory with the fundamental principles of gravity results in the modification of the uncertainty principle. In this study, we employ the extended uncertainty principle (EUP) with the maximum length derived from the cosmological particle horizon. The impact of this specific kind of modification is examined in a non-interacting electron gas system. We analytically derive the generalized relations for the degeneracy pressure and the bulk modulus. An intriguing finding is that the degeneracy pressure is reduced, as confirmed by the observed size of white dwarfs, which is smaller than what is predicted by the standard theory. Nevertheless, it is still capable of providing support against gravitational collapse. [ABSTRACT FROM AUTHOR]

The Rayleigh–Schrodinger method or more commonly called time independent perturbation theory is a powerful method to solve a Hamiltonian system with a relatively small perturbation [W. Nolting, Theoretical Physics 7: Quantum Mechanics–Methods and Applications (Springer International, 2017); F. Schwabl, Quantum Mechanics, 4th edn. (Springer, 2007)]. In this work, we make use of the Rayleigh–Schrodinger method to formulate a general method to calculate quasibound states of static spherically symmetric black hole solutions arising from modified theories of gravity. We discover that the Schwarzschild-like term corresponds to the main Hamiltonian while the modified theory of gravity's contribution of the spacetime metric corresponds to the perturbation terms. At the end, formula to calculate main Hamiltonian and perturbed Hamiltonian are discovered and presented. [ABSTRACT FROM AUTHOR]

One of the staple objectives of theoretical physics is to establish a reliable theory of quantum gravity. To achieve this goal, some fundamental scales are proposed in the modern era, e.g. two scales are proposed in the Snyder–de Sitter model. These two scales relate to measurement limits of the position and momentum. In this paper, we study the thermodynamic properties of the higher-dimensional Schwarzschild black hole in the context of rainbow gravity in the Snyder–de Sitter model within the presence and absence of rainbow gravity and compare our results for d = 4 with the results which are already derived in the previous literature [B. Hamil and B. C. Lütfüoğlu, Int. J. Geom. Methods Mod. Phys. 19, 2250047 (2022)]. We find the existence of the remnant temperature of the concerned black hole. Unlike the four-dimensional Schwarzschild black hole, the black hole in higher dimensions (d > 4) has two remnant temperatures. Moreover, we observe that in the rainbow gravity background a nonzero lower bound value of the temperature of the black hole exists. Finally, we analyze the thermal stability remnant conditions of the black hole by computing the heat capacity within this model. [ABSTRACT FROM AUTHOR]

In recent times, it has been perceived that incorporation of branes in higher dimensional theories of quantum gravity is very effective to differentiate those theories which successfully satisfy the swampland criteria. Moreover, warm inflation is considered to be most appropriate single scalar field inflationary model in the framework of swampland criteria. In this regard, we study two well-known Chaplygin gas (CG) models embedded in Randall–Sundrum braneworld. It is known that the de Sitter constraint is derived by taking into account Bousso's covariant entropy bound. We discuss the application of this result in the context of Chaplygin-brane models and find the condition on the slope of the potential. Furthermore, it is demonstrated that in view of warm inflation dynamics this condition remains essentially unchanged indicating the compatibility of the models with swampland criteria. In addition, we investigate the constraint on the warm inflation parameter imposed by the de Sitter conjecture which shows that the warm inflation is in accordance with de Sitter bound in the strong as well as in weak dissipative regime for both models of Chaplygin gas. [ABSTRACT FROM AUTHOR]

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck's constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology. [ABSTRACT FROM AUTHOR]

In our recently proposed quantum theory of gravity, the universe is made of 'atoms'" of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about 1 0 − 3 3 eV/c 2 , forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about 1 0 1 2 2 such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac's large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about 1 0 − 1 2 eV/c 2 . [ABSTRACT FROM AUTHOR]

Classical geometry can be described either in terms of a metric tensor g a b (x) or in terms of the geodesic distance σ 2 (x , x ′). Recent work, however, has shown that the geodesic distance is better suited to describe the quantum structure of spacetime. This is because one can incorporate some of the key quantum effects by replacing σ 2 by another function S [ σ 2 ] such that S [ 0 ] = L 0 2 is nonzero. This allows one to introduce a zero-point-length in the spacetime. I show that the geodesic distance can be an emergent construct, arising in the form of a correlator S [ σ 2 (x , y) ] = 〈 J (x) J (y) 〉 , of a pregeometric variable J (x) , which can be interpreted as the quantum density of spacetime events. This approach also shows why null surfaces play a special role in the interface of quantum theory and gravity. I describe several technical and conceptual aspects of this construction and discuss some of its implications. [ABSTRACT FROM AUTHOR]

Using the quantum theory of linearized gravity, gravitational interaction differential cross-sections of one fermion by another fermion, a photon and a scalar particle are calculated in the fermion rest frame. Then, according to the obtained results, it is shown that in the lab frame, the gravitational interaction depends on the spin of the moving particle and is independent of the spin of the rest particle. After that, on the dependency of the gravitational interaction of fermion–photon upon the various states of photons, polarization is discussed. [ABSTRACT FROM AUTHOR]

A new scenario of baryogenesis via the ratchet mechanism is proposed based on an analogy with the forced pendulum. The oscillation of the inflaton field during the reheating epoch after inflation plays the role of the driving force, while the phase 𝜃 of a scalar baryon field (a complex scalar field with baryon number) plays the role of the angle of the pendulum. When the inflaton is coupled to the scalar baryon, the behavior of the phase 𝜃 can be analogous to that of the angle of the forced pendulum. If the oscillation of the driving force is adjusted to the pendulum’s motion, a directed rotation of the pendulum is obtained with a nonvanishing value of 𝜃̇, which models successful baryogenesis since 𝜃̇ is proportional to the baryon number density. Similar ratchet models which lead to directed motion have been used in the study of molecular motors in biology. There, the driving force is supplied by chemical reactions, while in our scenario this role is played by the inflaton during the reheating epoch. [ABSTRACT FROM AUTHOR]

Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on (A)dS background. This fact can be generalized to higher dimensions. This degree of freedom is altered when a triadic Chern-Simons is introduced, giving rise to the self-dual massive gravity on (A)dS background. We present another physical system with partially massless symmetry and its connection with topologically massive gravity is discussed. [ABSTRACT FROM AUTHOR]

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a local field redefinition containing an infinite number of higher derivatives. It is also shown that the current-current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved. [ABSTRACT FROM AUTHOR]

Criteria for thermal stability of charged rotating black holes of any dimension are derived for horizon areas that are large relative to the Planck area (in these dimensions). The derivation is based on generic assumptions of quantum geometry, supported by some results of loop quantum gravity, and equilibrium statistical mechanics of the Grand Canonical ensemble. There is no explicit use of classical spacetime geometry in this analysis. The only assumption is that the mass of the black hole is a function of its horizon area, charge and angular momentum. Our stability criteria are then tested in detail against specific classical black holes in spacetime dimensions 4 and 5, whose metrics provide us with explicit relations for the dependence of the mass on the charge and angular momentum of the black holes. This enables us to predict which of these black holes are expected to be thermally unstable under Hawking radiation. [ABSTRACT FROM AUTHOR]

We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can calculate some physical quantities such as the expectation value of the area, that is, the volume of the two-dimensional Euclidean spacetime. We also consider the extensions of the model to higher dimensions. [ABSTRACT FROM AUTHOR]

The propagation of boson particles in a gravitational field described by the Brans-Dicke (BD) theory of gravity is analyzed. We derive the wave function of the scalar particles, and the effective potential experienced by the quantum particles considering the role of the varying gravitational coupling. Besides, we calculate the probability to find the scalar particles near the region where a naked singularity is present. The extremely high energy radiated in such a situation could account for the huge emitted power observed in gamma ray bursts (GRBs). [ABSTRACT FROM AUTHOR]

We discuss the implications of a purely classical (instead of quantum) theory of gravity for the primordial gravitational wave spectrum generated during inflation. We argue that for a scalar field driven inflation in a classical gravity the amplitude of the gravitational wave will be too small, irrespective of its primordial seed, to be detected in any forthcoming experiments. Therefore, a positive detection of the B-mode polarizations in the Cosmic Microwave Background (CMB) spectrum will naturally confirm the quantum nature of gravity itself. Furthermore there will be no upper limit on the scale of inflation in the case of classical gravity, and a high-scale model of inflation can easily bypass the observational constraints. [ABSTRACT FROM AUTHOR]

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present. [ABSTRACT FROM AUTHOR]

Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any particular set of field equations for the metric tensor, but only on covariance. It is derived in the linear case, but can be extended to any order of approximation in the metric deviation. In this formulation of the interaction of gravity with matter, angular momentum and momentum are conserved locally. [ABSTRACT FROM AUTHOR]

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated. [ABSTRACT FROM AUTHOR]

The entropie gravity scenario recently proposed by Erik Verlinde reproduced Newton's law of purely classical gravity yet the key assumptions of this approach all have quan-tum mechanical origins. As is typical for emergent phenomena in physics, the underlying, more fundamental physics often reveals itself as corrections to the leading classical be-havior. So one naturally wonders: where is h hiding in entropie gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its vari-ation law in order to obtain a self-consistent approach to the problem. Next we argue that since the concept of minimal length has been invoked in the Bekenstein entropie derivation, the generalized uncertainty principle (GUP), which is a direct consequence of the minimal length, should be taken into consideration in the entropie interpretation of gravity. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime where in the weak gravity limit the GUP modified entropy exhibits a logarithmic correction. When applying it to the entropie interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on h. Such deviation from the classical Newton's law may serve as a probe to the validity of entropie gravity. [ABSTRACT FROM AUTHOR]

This paper attempts to connect two new gravitational mechanisms: the Verlinde's holographic model of gravity and the modification of inertia resulting from a Hubble-scale Casimir effect (MiHsC) of McCulloch. First we give a short survey about how the holographic scenario can give the correct dynamics of the universe. The introduction of a two-holographic screens one comparable to the Hubble horizon and a second screen that takes into account the contribution of all the matter between the test particle and the observer gives directly the modified Friedmann acceleration equation for the dynamical evolution of the universe. Improvements of this equation using the quantum corrections will realize the inflation at high energy scales and the late-time acceleration (i.e. the accelerated expansion of the universe nowadays) obviating the dark energy. From both models we can derive a version of Modified Newtonian Dynamics (MOND) observed in the dynamics of the astronomical objects obviating the dark matter and explaining other astronomical anomalies. A first connection between both theories is given at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we calculate the heat flux passing through the horizon TS|rh and the difference of energy between the Einstein and Mailer prescription within the region M, in which is the region between outer horizon H+ and inner horizon H-, for the modified GHS solution, KLOPP solution and CLH solution. The formula EEinstein=Møller|M --∑∂M TS is obeyed for the mGHS solution and the KLOPP solution, but not for the CLH solution. Also, we suggest a RN-like stringy dyonic black hole solution, which comes from the KLOPP solution under a dual transformation, and its thermodynamical properties are the same as the KLOPP solution. [ABSTRACT FROM AUTHOR]

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity. [ABSTRACT FROM AUTHOR]

The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completely classical is misleading. In this paper, we argue that the entropic formulation provides new insights into the quantum nature of the inertia and the gravity. We use the entropic postulate to determine the quantum uncertainty in the law of inertia and in the law of gravity in the Newtonian Mechanics, the Special Relativity and in the General Relativity. These results are obtained by considering the most general quantum property of the matter represented by the Uncertainty Principle and by postulating an expression for the uncertainty of the entropy such that: (i) it is the simplest quantum generalization of the postulate of the variation of the entropy and (ii) it reduces to the variation of the entropy in the absence of the uncertainty. [ABSTRACT FROM AUTHOR]

Some quantum-cosmic scaling relations indicate that the MOND acceleration parameter a0 could be a fundamental quantity ruling the self-gravitating structures, ranging from stars and globular clusters up to superclusters of galaxies and the whole observed universe. We discuss such coincidence relations starting from the Dirac quantization condition ruling the masses of primordial black holes. [ABSTRACT FROM AUTHOR]

We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr's idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can also be derived from an ansatz of quantized entropy $\Delta S = 4\pi k \Delta R/{{^{-}{\!\!\!\!\lambda}}}$, which was suggested in a previous work to unify the black hole entropy formula and Verlinde's conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors. [ABSTRACT FROM AUTHOR]

The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity: one counting all allowed spin network labels j, m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation. [ABSTRACT FROM AUTHOR]

We present the explicit formulas relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed. [ABSTRACT FROM AUTHOR]

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the freezing of vacuum energy in such a dynamical energy-momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context. [ABSTRACT FROM AUTHOR]

We review on a recent construction of the on-shell supersymmetric brane action for the codimension-two branes with nonzero tension in the flux compactification of a 6D chiral gauged supergravity. On dimensionally reducing on 4D gauged supergravity for a new supersymmetric unwarped background with conical branes, we consider the modulus stabilization for determining the soft masses of the scalars localized on the branes and show that the bulk U(1)R provides a new mechanism for mediating the SUSY breaking. [ABSTRACT FROM AUTHOR]

We show that, by using resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get quantum field theoretic predictions for the UV fixed-point values of the dimensionless gravitational and cosmological constants. Connections to the phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter are discussed. [ABSTRACT FROM AUTHOR]

The effect of the ideal boundaries of infinite-genus surfaces and Dirichlet boundaries on the value of the string coupling is evaluated. It is demonstrated that the value coincides with the unified gauge coupling and it is not altered by the inclusion of curved four-dimensional spacetimes in the path integral for quantum gravity or boundaries with fractional dimension and nonzero harmonic measure. [ABSTRACT FROM AUTHOR]

Even though the chaotic inflation is one of the most popular inflation models for its simple dynamics and compelling resolutions to the initial condition problems, its realization in supergravity has been considered a challenging task. We discuss how the chaotic inflation dominated by the D-term can be induced in supergravity, which would give a new perspective on the inflation model building in supergravity. [ABSTRACT FROM AUTHOR]

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. Here we propose and analyse a generalisation of Heisenberg's equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenberg's equation turns out to be a delay-differential equation. [ABSTRACT FROM AUTHOR]

A novel mechanism of baryogenesis is proposed on the basis of the phase transition from the conformal invariant spacetime to the Einstein spacetime in quantum gravity. Strong-coupling gravitational excitations with dynamical mass about 1017 GeV are generated at the transition. They eventually decay into ordinary matters. We show that the low energy effective interactions between the gravitational potential describing the excitation and the non-conserving matter currents by the axial anomalies can explain matter asymmetry out of thermal equilibrium. [ABSTRACT FROM AUTHOR]

All thermodynamic quantities of the Reissner–Nordström (RN) black hole can be obtained from the dilaton and its potential of two-dimensional (2D) dilaton gravity. The dual relations of four thermodynamic laws are also established. Furthermore, the near-horizon thermodynamics of the extremal RN black hole is completely described by the Jackiw–Teitelboim theory which is obtained by perturbing around the AdS2-horizon. [ABSTRACT FROM AUTHOR]

Three decades of a deepening information paradox suggest the need to revise our basic physical framework. Multiple indicators point toward reassessment of the principle of locality: lack of a precise definition in quantum gravity, behavior of high-energy scattering, hints from strings and AdS/CFT, conundrums of quantum cosmology, and finally lack of good alternative resolutions of the paradox. A plausible conjecture states that the non-perturbative dynamics of gravity is unitary but nonlocal. String theory may directly address these issues but so far important aspects remain elusive. If this viewpoint is correct, critical questions are to understand the "correspondence" limit where nonlocal physics reduces to local quantum field theory, and beyond, to unveil principles of an underlying nonlocal theory. [ABSTRACT FROM AUTHOR]

We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length. Furthermore we give an explicit realization of an old proposal by Anderson and Finkelstein who argued that a fundamental length in nature implies unimodular gravity. Finally, using hand waving arguments we show that a minimal length might be related to the cosmological constant which, if this scenario is realized, is time dependent. [ABSTRACT FROM AUTHOR]

The string inspired higher dimensional theories suggest modification of Newton's law at submillimeter length scales. Inter-particle distances in white dwarf and neutron stars are 10-10 cms and 10-13 cms respectively, and therefore, the effects of short distance corrections to gravity deserve investigation. We show, by carrying out explicit analytical many-body calculations that, in the presence of corrections, the normal state of these compact stars become metastable. The actual quantum mechanical ground state of the stars turns out to be unstable. However, the tunneling probability to the unstable ground state is so small that the stars may remain trapped in the metastable state practically forever. [ABSTRACT FROM AUTHOR]

We have applied the method of dualization to construct the coset realization of the bosonic sector of the $\mathcal{N}=2$, D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction. [ABSTRACT FROM AUTHOR]

We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in terms of a linear system for the fluxes and the geometry of spacetime. The solutions of this linear system express some of the fluxes in terms of the spacetime geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. We also present some of the recent applications like the classification of maximally supersymmetric G-backgrounds in IIB, this includes the most general pp-wave solution preserving 1/2 supersymmetry, and the classification of N = 31 backgrounds in ten and eleven dimensions. [ABSTRACT FROM AUTHOR]

Here we present explicit expressions for quantum fluctuations of spacetime in the case of (4+n)-dimensional spacetimes, and consider their holographic properties and some implications for clocks, black holes and computation. We also consider quantum fluctuations and their holographic properties in ADD model and estimate the typical size and mass of the clock to be used in precise measurements of spacetime fluctuations. Numerical estimations of phase incoherence of light from extra-galactic sources in ADD model are also presented. [ABSTRACT FROM AUTHOR]

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean geometry. We suggest that this mechanism may hint at the origin of time in the fundamental theory of quantum gravity. [ABSTRACT FROM AUTHOR]

The emergence of quantum-gravity induced corrective terms for the probability of emission of a particle from a black hole in the Parikh–Wilczek tunneling framework is studied. It is shown, in particular, how corrections might arise from modifications of the surface gravity due to near horizon Planck-scale effects. Our derivation provides an example of the possible linking between Planck-scale departures from Lorentz invariance and the appearance of higher order quantum gravity corrections in the black-hole entropy-area relation. [ABSTRACT FROM AUTHOR]

In this paper two consequences of the generalized uncertainty principle (GUP) are discussed in a heuristic manner. Both could be regarded as the evidences that prefer the cosmic censorship hypothesis (CCH). The first one is that the second law tends to decline the massless charged particles if the effects of the GUP on the thermodynamics of a de Sitter spacetime are considered. This weakens the threat to the horizon of an extreme charged black hole. The second one is that the uv/ir correspondence provides a constraint on the relation between the energy and the size of a system, which is incompatible to the naked singularities. [ABSTRACT FROM AUTHOR]

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional "spurious" or "unphysical" pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory. [ABSTRACT FROM AUTHOR]

We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action. [ABSTRACT FROM AUTHOR]

We propose a new approach to the quantum theory of gravitation, in which the point sets of regions of spacetime are replaced by objects in a category. The objects can be constructed as limits of spin foam models, thus directly connecting to approximations to general relativity which have already been studied, and leading to a mathematically natural interpretation of the meaning of the triangulations in the spin foam models. The physical motivation for our proposal is a connection between ideas about the limited amount of information which can flow from one region to another in General Relativity, an analysis of the problem of the infinities in QFT, and the relational or categorical approach to topology in abstract homotopy theory and algebraic geometry. [ABSTRACT FROM AUTHOR]

This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on the non-trivial part of the gravitational response, which is to the large momenta propagating around a closed loop. By taking a limiting case one can give a simple geometric description of this gravitational response. This is calculated in detail for the example of a closed Feynman loop in the form of a trefoil knot. The results show that when the magnitude of the momentum passes a certain threshold value, non-trivial gravitational configurations of the knot play an important role. [ABSTRACT FROM AUTHOR]

We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity. [ABSTRACT FROM AUTHOR]