scholarly journals Contextual extensions of quantum gravity models

2021 ◽  
pp. 2150085
Author(s):  
Xiao-Kan Guo
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Hidden Variables ◽  
Gravity Models

We present a simple way of incorporating the structure of contextual extensions into quantum gravity models. The contextual extensions of [Formula: see text]-algebras, originally proposed for contextual hidden variables, are generalized to the cones indexed by the contexts and their limit in a category. By abstracting the quantum gravity models as functors, we study the contextual extensions as the categorical limits of these functors in several quantum gravity models. Such contextual extensions of quantum gravity models are useful for building topos-theoretic models of quantum gravity.

scholarly journals COMBINATORIAL AND TOPOLOGICAL PHASE STRUCTURE OF NON-PERTURBATIVE n-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2109-2121
Author(s):  
M. CARFORA ◽  
M. MARTELLINI ◽  
A. MARZUOLI
Keyword(s):  
Quantum Gravity ◽  
Phase Structure ◽  
Gravity Models ◽  
Topological Phase ◽  
Geometrical Characterization ◽  
Homotopy Types ◽  
Geometrical Constraints ◽  
Riemannian Geometries

We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

scholarly journals Quantum Gravity Effects in Statistical Mechanics with Modified Dispersion Relation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Shovon Biswas ◽  
Mir Mehedi Faruk
Keyword(s):  
Dispersion Relation ◽  
Quantum Gravity ◽  
Statistical Mechanics ◽  
Planck Scale ◽  
Maximum Energy ◽  
Gravity Models ◽  
Momentum Scale ◽  
Modified Dispersion Relation ◽  
Gravity Effects ◽  
Photon Gas

Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper, we resort to the methods of statistical mechanics in order to determine the effects of a deformed dispersion relation along with an upper bound in the partition function that maximum energy and/or momentum scale can have on the thermodynamics of photon gas. We also analyzed two distinct quantum gravity models in this paper.

scholarly journals Probing quantum gravity effects with quantum mechanical oscillators

2020 ◽  
Vol 74 (9) ◽  
Author(s):  
Michele Bonaldi ◽  
Antonio Borrielli ◽  
Avishek Chowdhury ◽  
Gianni Di Giuseppe ◽  
Wenlin Li ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Quantum Physics ◽  
Deformation Parameter ◽  
Thermal State ◽  
Classical Trajectory ◽  
Point Of View ◽  
Gravity Models ◽  
Gravity Effects ◽  
The Status ◽  
Mechanical Oscillators

Abstract Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that account for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the basis of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization. Graphical abstract

scholarly journals Black hole spectroscopy from loop quantum gravity models

2015 ◽  
Vol 92 (12) ◽  
Author(s):  
Aurelien Barrau ◽  
Xiangyu Cao ◽  
Karim Noui ◽  
Alejandro Perez
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Gravity Models

scholarly journals FRG analysis of a multi-matrix model for 3d Lorentzian quantum gravity

2020 ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Antonio Duarte Pereira ◽  
Astrid Eichhorn
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Recent Progress ◽  
Gravity Models ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Tensor Models ◽  
Practical Tool

At criticality, discrete quantum gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional Renormalization Group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB-interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality.

scholarly journals Comment on Coleman-DeLuccia instantons

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Thomas Banks ◽  
Bingnan Zhang
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Transition Probabilities ◽  
Detailed Balance ◽  
De Sitter Space ◽  
Positive Energy ◽  
De Sitter ◽  
Finite Area ◽  
Quantum Models

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

One-loop renormalization in quantum gravity

2021 ◽  
pp. 474-487
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
General Relativity ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Detailed Analysis ◽  
Polynomial Model ◽  
Similar Calculation ◽  
Higher Derivative ◽  
Gauge Fixing ◽  
Fourth Derivative ◽  
Detailed Derivation

This chapter demonstrates the basic methods of one-loop calculations in quantum gravity. Basing its discussion on the general results obtained in chapter 10, it first presents a detailed analysis of the gauge-fixing dependence of one-loop divergences in quantum general relativity and higher-derivative models of quantum gravity. After that, a detailed derivation of divergences in quantum general relativity is given, with the simplest parametrization of the quantum metric and minimal gauge fixing. One-loop divergences in the general (non-conformal) fourth-derivative quantum gravity are then derived in less detail. For a similar calculation in the superrenormalizable polynomial model (superrenormalizable gravity), the chapter just presents and discusses the final result.

scholarly journals GRAVITY AS BF THEORY PLUS POTENTIAL

2009 ◽  
Vol 24 (15) ◽  
pp. 2776-2782 ◽  
Author(s):  
KIRILL KRASNOV
Keyword(s):  
General Relativity ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Alternative Formulation ◽  
Potential Term ◽  
Bf Theory ◽  
Spin Foam Models ◽  
Spin Foam ◽  
To Come

Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the potential is taken to be infinitely steep one recovers general relativity. For a generic potential the theory still describes gravity in that it propagates just two graviton polarizations. The arising class of theories is of the type amenable to spin foam quantization methods, and, we argue, may allow one to come to terms with renormalization in the spin foam context.

scholarly journals TENSOR MODELS AND HIERARCHY OF n-ARY ALGEBRAS

2011 ◽  
Vol 26 (19) ◽  
pp. 3249-3258 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Algebraic Structure ◽  
The Other ◽  
Invariant Form ◽  
Infinitesimal Symmetry ◽  
Tensor Models ◽  
Symmetry Transformations

Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator, and the 3-ary algebra symmetry reported in the previous paper is just a single sector of the whole structure. The condition for the Leibnitz rules of the n-ary algebras is discussed from the perspective of the invariance of the underlying algebra under the n-ary transformations. It is shown that the n-ary transformations which keep the underlying algebraic structure invariant form closed finite n-ary Lie subalgebras. It is also shown that, in physical settings, the 3-ary transformation practically generates only local infinitesimal symmetry transformations, and the other more nonlocal infinitesimal symmetry transformations of the tensor models are generated by higher n-ary transformations.

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