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Symmetry
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Symmetry and Quantum Gravity
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Symmetry and Quantum Gravity

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 May 2020) | Viewed by 17184

Special Issue Editor

Dr. Giovanni Modanese

E-Mail Website
Guest Editor
Faculty of Science and Technology, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Interests: quantum and classical field theory; gravitation; complex systems in connection to social science and economics; mathematical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In quantum field models of electro-weak and strong interactions, "internal" symmetries have played a fundamental role, even before the epoch of gauge theories: Just think of the isospin symmetry, current algebra, Cabibbo angle, etc. For effective theories of quantum gravity (QG), one expects spacetime symmetries to play an equally important role, not only in the weak-field expansion on a fixed background, but also when strong fluctuations of the spacetime geometry are admitted (with the ensuing conceptual/interpretation problems). The most natural approaches for describing these situations are based on functional integrals and renormalization group techniques, either in the metric formalism or with Regge calculus or dynamical triangulations. We thus invite to consider such approaches, summarize their status and propose advances, also at the computational/simulation level, with special attention for the role of symmetries and their phenomenological consequences. The underlying action should be Einstein's action or one of its extensions. In this context, theories "beyond spacetime" like loop QG or group QG could be considered with regard to their "emergent spacetime" properties.

Dr. Giovanni Modanese
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum gravity
  • effective quantum gravity
  • path integrals, functional integrals
  • Regge calculus
  • general covariance
  • diffeomorphisms
  • metric formulation
  • Einstein action
  • gravitons

Published Papers (7 papers)

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Research

33 pages, 361 KiB  
Article
The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity
by Selman Ipek and Ariel Caticha
Symmetry 2020, 12(8), 1324; https://doi.org/10.3390/sym12081324 - 07 Aug 2020
Cited by 4 | Viewed by 2096
Abstract
Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum [...] Read more.
Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
63 pages, 758 KiB  
Article
Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit
by Max Niedermaier
Symmetry 2020, 12(5), 752; https://doi.org/10.3390/sym12050752 - 06 May 2020
Cited by 8 | Viewed by 2218
Abstract
A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the [...] Read more.
A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
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8 pages, 258 KiB  
Article
Summing over Spacetime Dimensions in Quantum Gravity
by Erik Curiel, Felix Finster and Jose Maria Isidro
Symmetry 2020, 12(1), 138; https://doi.org/10.3390/sym12010138 - 09 Jan 2020
Cited by 9 | Viewed by 1849
Abstract
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand [...] Read more.
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
13 pages, 261 KiB  
Article
Spacetime and Deformations of Special Relativistic Kinematics
by José Manuel Carmona, José Luis Cortés and José Javier Relancio
Symmetry 2019, 11(11), 1401; https://doi.org/10.3390/sym11111401 - 12 Nov 2019
Cited by 14 | Viewed by 2089
Abstract
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction [...] Read more.
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction processes, for which absolute locality in terms of canonical spacetime coordinates is lost. We discuss the different alternatives for observable effects in the propagation of a particle over very large distances that emerge from the new notion of spacetime. A central ingredient in the discussion is the cluster decomposition principle, which can be used to favor some alternatives over the others. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
11 pages, 572 KiB  
Article
Exploiting Weak Field Gravity-Maxwell Symmetry in Superconductive Fluctuations Regime
by Giovanni Alberto Ummarino and Antonio Gallerati
Symmetry 2019, 11(11), 1341; https://doi.org/10.3390/sym11111341 - 01 Nov 2019
Cited by 15 | Viewed by 2871
Abstract
We study the behaviour of a superconductor in a weak static gravitational field for temperatures slightly greater than its transition temperature (fluctuation regime). Making use of the time-dependent Ginzburg–Landau equations, we find a possible short time alteration of the static gravitational field in [...] Read more.
We study the behaviour of a superconductor in a weak static gravitational field for temperatures slightly greater than its transition temperature (fluctuation regime). Making use of the time-dependent Ginzburg–Landau equations, we find a possible short time alteration of the static gravitational field in the vicinity of the superconductor, providing also a qualitative behaviour in the weak field condition. Finally, we compare the behaviour of various superconducting materials, investigating which parameters could enhance the gravitational field alteration. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
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12 pages, 648 KiB  
Article
Metrics with Zero and Almost-Zero Einstein Action in Quantum Gravity
by Giovanni Modanese
Symmetry 2019, 11(10), 1288; https://doi.org/10.3390/sym11101288 - 14 Oct 2019
Cited by 4 | Viewed by 1850
Abstract
We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action S E ≪ ℏ . This is obtained through a Metropolis algorithm with weight exp ( − β 2 S E 2 ) and [...] Read more.
We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action S E ≪ ℏ . This is obtained through a Metropolis algorithm with weight exp ( − β 2 S E 2 ) and β ≫ ℏ − 1 . The squared action in the exponential allows to circumvene the problem of the non-positivity of S E . The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition S E = 0 exactly, or in certain cases even the stronger condition R ( x ) = 0 for any x . All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler’s “spacetime foam”. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
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51 pages, 737 KiB  
Article
Vacuum Condensate Picture of Quantum Gravity
by Herbert W. Hamber
Symmetry 2019, 11(1), 87; https://doi.org/10.3390/sym11010087 - 14 Jan 2019
Cited by 13 | Viewed by 3675
Abstract
In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the [...] Read more.
In quantum gravity perturbation theory in Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge–Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale ξ in many ways analogous to the scaling violation parameter Λ M ¯ S of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments. Full article
(This article belongs to the Special Issue Symmetry and Quantum Gravity)
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