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The article discusses the possibility of breaking Penrose's weak cosmic censorship conjecture in black hole collisions in higher dimensions using the technique called large D. It is stated that in black hole collisions with sufficient angular momentum, the resulting black hole is unstable and can split into two, creating a divergent curvature throat. The relationship between physics at different scales in a physical system is also mentioned, as well as the need to quantize theories to understand physics at the microscopic scale. Additionally, the need for a quantum theory of gravity to make predictions at increasingly higher energies is mentioned. [Extracted from the article]

Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell systems. Various germane issues and all-loop renormalizability have been addressed. In the present work we make further progress by carrying out several additional tasks. Firstly, we present an alternative 4D-covariant derivation of the physical state condition by examining gauge choice-independence of a scattering amplitude. To this end, a careful dichotomy between the ordinary, and large gauge symmetries is required and appropriate gauge-fixing of the ordinary symmetry must be performed. Secondly, vacuum energy is analyzed in a finite-temperature setup. A variant optimal perturbation theory is implemented to two-loop. The renormalized mass determined by the optimal perturbation theory turns out to be on the order of the temperature, allowing one to avoid the cosmological constant problem. The third task that we take up is examination of the possibility of asymptotic freedom in finite-temperature quantum electrodynamics. In spite of the debates in the literature, the idea remains reasonable. [ABSTRACT FROM AUTHOR]

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter t (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed. [ABSTRACT FROM AUTHOR]

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families. [ABSTRACT FROM AUTHOR]

We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter Δ. We show that the linear scalar field theory is reconstructed in the large spin limit. For Δ = 1 , a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter Δ → 0 , the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity. [ABSTRACT FROM AUTHOR]

A fundamental problem of Einsteins theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in quantum gravity, supercomputers are now playing an important role in understanding the resolution of big bang and black hole singularities. Using supercomputers, explorations of the very genesis of space and time from quantum geometry are revealing a novel picture of what lies beyond classical singularities and the new physics of the birth of our universe. [ABSTRACT FROM AUTHOR]

Given two sets S1, S2 and unital C*-algebras A1, A2 of functions thereon, we show that a map σ:S1⟶S2 can be lifted to a continuous map σ¯:specA1⟶specA2 iff σ*A2:={σ*f|f∈A2}⊆A1. Moreover, σ¯ is unique if existing, and injective iff σ*A2 is dense. Then, we apply these results to loop quantum gravity and loop quantum cosmology. For all usual technical conventions, we decide whether the cosmological quantum configuration space is embedded into the gravitational one; indeed, both are spectra of some C*-algebras, say, Acosm and Agrav, respectively. Typically, there is no embedding, but one can always get an embedding by the defining Acosm:=C*(σ*Agrav), where σ denotes the embedding between the classical configuration spaces. Finally, we explicitly determine C*(σ*Agrav) in the homogeneous isotropic case for Agrav generated by the matrix functions of parallel transports along analytic paths. The cosmological quantum configuration space so equals the disjoint union of R and the Bohr compactification of R, appropriately glued together. [ABSTRACT FROM AUTHOR]

In this paper, using the new type of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which has predicted both a minimal length uncertainty and a maximal observable momentum,1 first, we obtain the maximally localized states and express their connections to [P. Pedram, Phys. Lett. B 714, 317 (2012)]. Then, in the context of our proposed GUP and using the generalized Schrödinger equation, we solve some important problems including particle in a box and one-dimensional hydrogen atom. Next, implying modified Bohr-Sommerfeld quantization, we obtain energy spectra of quantum harmonic oscillator and quantum bouncer. Finally, as an example, we investigate some statistical properties of a free particle, including partition function and internal energy, in the presence of the mentioned GUP. [ABSTRACT FROM AUTHOR]

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects. [ABSTRACT FROM AUTHOR]

Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space–time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches. [ABSTRACT FROM AUTHOR]

The Duflo map is a valuable tool for operator ordering in contexts in which the Kirillov–Kostant–Souriau bracket and its quantization play a role. It has beautiful properties on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. In the present work, we focus on its action beyond this subspace: We calculate the image of the exponential map, to obtain a certain deformation of SU(2), and we discuss and compare modifications of its action on non-invariant elements. Also, an application to the calculation of Chern–Simons theory expectation values is discussed. [ABSTRACT FROM AUTHOR]

Recent developments in quantum gravity have shown the Lorentzian treatment to be a fruitful approach towards the emergence of macroscopic space-times. In this paper, we discuss another related aspect of the Lorentzian treatment: we argue that collective quantum coherence may provide a simple mechanism for highlighting symmetric configurations over generic non-symmetric ones. After presenting the general framework of the mechanism, we show the phenomenon in some concrete simple examples in the randomly connected tensor network, which is tightly related to a certain model of quantum gravity, i.e., the canonical tensor model. We find large peaks at configurations invariant under Lie-group symmetries as well as a preference for charge quantization, even in the Abelian case. In future study, this simple mechanism may provide a way to analyze the emergence of macroscopic space-times with global symmetries as well as various other symmetries existing in nature, which are usually postulated. [ABSTRACT FROM AUTHOR]

In the canonical approach to quantization of gravity, one often uses relational clock variables and an interpretation in terms of conditional probabilities to overcome the problem of time. In this essay, we show that these suffer from serious conceptual issues. [ABSTRACT FROM AUTHOR]

In the study of covariant wave equations, linear gravity manifests itself through the metric deviation and a two-point vector potential itself constructed from and its derivatives. The simultaneous presence of the two gravitational potentials is noncontradictory. Particles also assume the character of quasiparticles and carries information about the matter with which it interacts. We consider the influence of on the dispersion relations of the particles involved, the particles' motion, quantum tunneling through a horizon, radiation, energy-momentum dissipation and flux quantization. [ABSTRACT FROM AUTHOR]

Full general relativity is almost certainly ‘chaotic’. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables . This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity. [ABSTRACT FROM AUTHOR]

Hořava's quantum gravity at a Lifshitz point is a theory intended to quantize gravity by using traditional quantum field theories. To avoid Ostrogradsky's ghosts, a problem that has been facing in quantization of general relativity since the middle of 1970's, Hořava chose to break the Lorentz invariance by a Lifshitz-type of anisotropic scaling between space and time at the ultra-high energy, while recovering (approximately) the invariance at low energies. With the stringent observational constraints and self-consistency, it turns out that this is not an easy task, and various modifications have been proposed, since the first incarnation of the theory in 2009. In this review, we shall provide a progress report on the recent development of Hořava gravity. In particular, we first present four so far most-studied versions of Hořava gravity, by focusing first on their self-consistency and then their consistency with experiments, including the solar system tests and cosmological observations. Then, we provide a general review on the recent development of the theory in three different but also related areas: (i) universal horizons, black holes and their thermodynamics, (ii) nonrelativistic gauge/gravity duality and (iii) quantization of the theory. The studies in these areas can be easily generalized to other gravitational theories with broken Lorentz invariance. [ABSTRACT FROM AUTHOR]

We show using simple arguments, that the conceptual triad of a classical black hole, semi-classical Hawking emission and geometry quantization is inherently, mutually incompatible. Presence of any two explicitly violates the third. We argue that geometry quantization, if realized in nature, magnifies the quantum gravity features hugely to catapult them into the realm of observational possibilities. We also explore a quantum route towards extremality of the black holes. [ABSTRACT FROM AUTHOR]

In this paper, I propose a quantization of gravity that leads to photons mediated gravitation. The quantization of general relativity depends now on the modified special relativity [A. Almosallami, e-print viXra:1111.0001v1 (2011); e-print viXra:1401.0043 [High Energy Particle Physics] (2014)], which introduces a new interpretation of the Lorentz transformation equations depending on quantum theory (Copenhagen school) [A. AlMosallami, IJSER 5, 128 (2014); Int. J. Mod. Theor. Phys. 3, 44 (2014); e-print viXra:1111.0001v1 [Relativity and Cosmology] (2011); e-print viXra:1401.0043 [High Energy Particle Physics] (2014); IJSER 5, 451 (2014)]. In these new transformations, I propose there is no space-time continuum, as in special relativity; it is only time, and space is invariant. This new interpretation of the Lorentz transformations leads to the transformation being vacuum energy dependent instead of relative velocity dependent as in Einstein's interpretation of the Lorentz transformation equations of the theory of special relativity. Furthermore, the Lorentz factor is equivalent to the refractive index in optics. In this new interpretation of the Lorentz transformations, I refuse the reciprocity principle adopted by Einstein in the theory of special relativity. Refusing the reciprocity principle in this theory leads to the disappearance of all the paradoxes of the theory of special relativity: The Twin paradox, Ehrenfest paradox, the Ladder paradox, and Bell's spaceship paradox. Furthermore, according to my interpretation, one could explain the experimental results of quantum tunneling and entanglement (spooky action), Casimir effect, and Hartman effect. The new interpretation of the Lorentz transformation equations leads also to the wave-particle duality as in the quantum theory, and thus agrees with Heisenberg uncertainty principle. The generalization of the transformation leads also to the concept of acceleration or deceleration as vacuum fluctuations as in the quantum field theory. In the proposed quantized force, the force is given as a function of frequency, where in this paper I defined the relativistic momentum as a function of frequency equivalent to the relativistic kinetic energy held by a body and time, and then the quantized force is given as the first derivative of the momentum with respect to time. Subsequently, I introduce Newton's second law as its relativistic quantized force. Further, I introduce the relativistic quantized inertial force, and then, by my equivalence principle, which agrees completely with the experimental results of quantum field theory, I introduce the relativistic quantized gravitational force, and the quantized time dilation. [ABSTRACT FROM AUTHOR]

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposedWeyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. [ABSTRACT FROM AUTHOR]

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)n and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for R2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann- Hall transform, can serve as basis of the former. [ABSTRACT FROM AUTHOR]

We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee–Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable. [ABSTRACT FROM AUTHOR]

Given a group $${G}$$ , and an abelian $${C^*}$$ -algebra $${\mathfrak{A}}$$ , the antihomomorphisms $${\Theta\colon G\rightarrow {\mathrm{Aut}}(\mathfrak{A})}$$ are in one-to-one with those left actions $${\Phi\colon G\times {\mathrm{Spec}}(\mathfrak{A})\rightarrow {\mathrm{Spec}}(\mathfrak{A})}$$ whose translation maps $${\Phi_g}$$ are continuous; whereby continuities of $${\Theta}$$ and $${\Phi}$$ turn out to be equivalent if $${\mathfrak{A}}$$ is unital. In particular, a left action $${\phi\colon G \times X\rightarrow X}$$ can be uniquely extended to the spectrum of a $${C^*}$$ -subalgebra $${\mathfrak{A}}$$ of the bounded functions on $${X}$$ if $${\phi_g^*(\mathfrak{A})\subseteq \mathfrak{A}}$$ holds for each $${g\in G}$$ . In the present paper, we apply this to the framework of loop quantum gravity. We show that, on the level of the configuration spaces, quantization and reduction in general do not commute, i.e., that the symmetry-reduced quantum configuration space is (strictly) larger than the quantized configuration space of the reduced classical theory. Here, the quantum-reduced space has the advantage to be completely characterized by a simple algebraic relation, whereby the quantized reduced classical space is usually hard to compute. [ABSTRACT FROM AUTHOR]

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below. [ABSTRACT FROM AUTHOR]

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity. [ABSTRACT FROM AUTHOR]

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. [ABSTRACT FROM AUTHOR]

Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL ( 2 , C ) Chern–Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity. [ABSTRACT FROM AUTHOR]

Several approaches to quantizing general relativity suggest that quantum gravity at very short distances behaves effectively as a two-dimensional theory. The mechanism of this dimensional reduction is not yet understood. We attempt to explain it by studying the phase space of a test particle coupled to a gravitational field. The general relativity constraints relate the particle energy-momentum to some curvature invariants taking values in a group manifold. Some directions in the resulting momentum space turn out to be compact, which leads to a kind of 'inverse Kaluza-Klein reduction' at short distances. [ABSTRACT FROM AUTHOR]

In this work, we derive the asymptotic quasi-normal modes of a Banados-Teitelboim-Zanelli (BTZ) black hole using a quantum field theoretic Lagrangian. The BTZ black hole is a very popular system in the context of 2 + 1-dimensional quantum gravity. However, to our knowledge the quasi-normal modes of the BTZ black hole have been studied only in the classical domain. Here we show a way to quantize the quasi-normal modes of the BTZ black hole by mapping it to the Bateman-Feschbach-Tikochinsky oscillator and the Caldirola-Kanai oscillator. We have also discussed a couple of other black hole potentials to which this method can be applied. [ABSTRACT FROM AUTHOR]