Symmetries in General Relativity 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 2024) | Viewed by 1437

Special Issue Editors


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Guest Editor
Departamento de Engenharia Informática e Sistemas de Informação, Universidade Lusófona de Humanidades e Tecnologias, Av. do Campo Grande 376, 1749-024 Lisbon, Portugal
Interests: loop quantum gravity; quantum cosmology; group theory; quantum gravity

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Guest Editor
Faculty of Physics, University of Belgrade, Studentski Trg 12, SR-11001 Belgrade, Serbia
Interests: noncommutative geometry

Special Issue Information

Dear Colleagues,

Symmetries are important tools for the study of GR and QG, since symmetry-reduced models play an important role. When the spacetime metric is invariant under finite Lie group transformations or under two-dimensional diffeomorphism transformations, one obtains tractable models, which can be a cosmological mini-superspace model or a 2D field theory model for a black hole formation.

Another use of symmetries is to assume that the diffeomorphism invariance is valid at large distances, while at the Planck length scales, we have some other symmetry. One way to achieve this is by changing the spacetime manifold structure, and some of the current approaches are:

  1. Changing the smooth manifold to a piecewise linear manifold and conserving the local Lorentz invariance. This yields the spin foam and Regge state-sum/state-integral models of QG;
  2. Replacing the local Lorentz group with some categorical group or a quantum group;
  3. Using a noncommutative manifold.

In this Special Issue, we welcome the submission of papers on the following topics:

  • Classical and quantum mini-superspace models;
  • Classical and quantum midi-superspace models;
  • 2D models of black holes;
  • Higher gauge theory formulations of GR;
  • State-sum models of QG;
  • Noncommutative geometry formulations of GR.

Papers on related topics will be also considered—for example, deformed GR theories. 

Prof. Dr. Aleksandar Mikovic
Prof. Dr. Maja Burić
Guest Editors

Manuscript Submission Information

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Keywords

  • mini-superspace models
  • midi-superspace models
  • 2D dilation gravity models
  • higher gauge theory
  • state-sum models
  • noncommutative geometry
  • deformed GR

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Published Papers (1 paper)

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Review

8 pages, 255 KiB  
Review
Gravity = Yang–Mills
by Roberto Bonezzi, Christoph Chiaffrino, Felipe Díaz-Jaramillo and Olaf Hohm
Symmetry 2023, 15(11), 2062; https://doi.org/10.3390/sym15112062 - 14 Nov 2023
Cited by 6 | Viewed by 934
Abstract
This essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang–Mills [...] Read more.
This essay’s title is justified by discussing a class of Yang–Mills-type theories of which standard Yang–Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of homotopy algebras, where conventional Yang–Mills theory is the tensor product Kg of a ‘kinematic’ algebra K with a color Lie algebra g. The larger class of Yang–Mills-type theories are given by the tensor product of K with more general Lie-type algebras, of which K itself is an example, up to anomalies that can be canceled for the tensor product with a second copy K¯. Gravity is then given by KK¯. Full article
(This article belongs to the Special Issue Symmetries in General Relativity and Quantum Gravity)
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