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Symmetry
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Symmetry in Classical and Quantum Gravity and Field Theory
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Symmetry in Classical and Quantum Gravity and Field Theory

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

Deadline for manuscript submissions: 30 April 2025 | Viewed by 9645

Special Issue Editor

Dr. Saeed Rastgoo

E-Mail Website
Guest Editor
Departments of Physics and Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2E1, Canada
Interests: classical and quantum gravity; black holes; gauge and constrained systems; mathematical physics

Special Issue Information

Dear Colleagues,

Symmetry is arguably one of the most important features of nature, and the theories that describe it include classical and quantum field theories. Symmetry provides elegant conceptual clarity about the nature and structure of these theories. Its importance, however, is not only limited to the conceptual realm. It also has a crucial role at the computational level. In fact, many of the results that are rather easily computed using symmetry methods are either quite difficult or even impossible to come by without utilizing symmetry.

The deep connection between symmetries and mathematics, particularly algebra, group theory and topology, is another aspect that renders symmetry a fascinating investigated subject not only limited to physicists but also relative to mathematicians. Symmetry is also a central topic in the philosophy of physics. In particular, spacetime and internal symmetries are subjects of much philosophical arguments and speculations about the nature of physical reality.

As it is clear from the title, this Special Issue of Symmetry features articles about the physical, mathematical and conceptual role of symmetry in quantum theory and gravity and, in particular, in classical gravity, quantum gravity, high energy physics, black holes and cosmology. We are cordially inviting colleagues, physicists, mathematicians and philosophers of science to submit their works with regard to the above subject to this Special Issue.

Dr. Saeed Rastgoo
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

  • classical and quantum gravity
  • quantum field theory
  • symmetry and group theory
  • classical and quantum cosmology
  • classical and quantum black holes lie groups
  • diffeomorphisms
  • constrained and gauge systems
  • path integral and BRST quantization

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

25 pages, 665 KiB  
Article
About a Classical Gravitational Interaction in a General Non-Inertial Reference Frame: Applications on Celestial Mechanics and Astrodynamics
by Daniel Condurache, Mihail Cojocari and Ionuț Popa
Symmetry 2025, 17(3), 368; https://doi.org/10.3390/sym17030368 - 28 Feb 2025
Viewed by 239
Abstract
This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals [...] Read more.
This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals of motion for a system of many particles in arbitrary non-inertial and barycentric rotating reference frames. These first integrals provide a kinematic and geometric visualization of motion in non-inertial frames. Additionally, a generalized potential energy function is presented for broader applicability. For the gravitational two-body problem, the paper delivers a closed-form, coordinate-free solution for the motion of each body relative to the original frame. Consequently, sufficient conditions for stability against collisions are established within the context of the two-body problem in a non-inertial reference frame. Furthermore, the paper examines the relative orbital motion of spacecraft, presenting a closed-form and coordinate-free solution in the local vertical local horizontal (LVLH) non-inertial frame, which is centered on the center of mass of the main spacecraft. Full article
(This article belongs to the Special Issue Symmetry in Classical and Quantum Gravity and Field Theory)
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21 pages, 337 KiB  
Article
Planck Length Emerging as the Invariant Quantum Minimum Effective Length Determined by the Heisenberg Uncertainty Principle in Manifestly Covariant Quantum Gravity Theory
by Claudio Cremaschini and Massimo Tessarotto
Symmetry 2024, 16(8), 1042; https://doi.org/10.3390/sym16081042 - 14 Aug 2024
Viewed by 1290
Abstract
The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires [...] Read more.
The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of O1, the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle. Full article
(This article belongs to the Special Issue Symmetry in Classical and Quantum Gravity and Field Theory)
25 pages, 309 KiB  
Article
Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension
by Øyvind G. Grøn
Symmetry 2024, 16(5), 564; https://doi.org/10.3390/sym16050564 - 5 May 2024
Cited by 2 | Viewed by 956
Abstract
I deduce an exact and analytic Bianchi type I solution of Einstein’s field equations, which generalizes the isotropic ΛCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the ΛCDM [...] Read more.
I deduce an exact and analytic Bianchi type I solution of Einstein’s field equations, which generalizes the isotropic ΛCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the ΛCDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the ΛCDM universe model. Although such generalizations of the isotropic ΛCDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic ΛCDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic large-scale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions—even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension. Full article
(This article belongs to the Special Issue Symmetry in Classical and Quantum Gravity and Field Theory)
38 pages, 579 KiB  
Article
Groups of Coordinate Transformations between Accelerated Frames
by Georgy I. Burde
Symmetry 2023, 15(6), 1226; https://doi.org/10.3390/sym15061226 - 8 Jun 2023
Viewed by 2121
Abstract
The analysis of the present paper reveals that, besides the relativistic symmetry expressed by the Lorentz group of coordinate transformations which leave invariant the Minkowski metric of space-time of inertial frames, there exists one more relativistic symmetry expressed by a group of coordinate [...] Read more.
The analysis of the present paper reveals that, besides the relativistic symmetry expressed by the Lorentz group of coordinate transformations which leave invariant the Minkowski metric of space-time of inertial frames, there exists one more relativistic symmetry expressed by a group of coordinate transformations leaving invariant the space-time metric of the frames with a constant proper-acceleration. It is remarkable that, in the flat space-time, only those two relativistic symmetries, corresponding to groups of continuous transformations leaving invariant the metric of space-time of extended rigid reference frames, exist. Therefore, the new relativistic symmetry should be considered on an equal footing with the Lorentz symmetry. The groups of transformations leaving invariant the metric of the space-time of constant proper-acceleration are determined using the Lie group analysis, supplemented by the requirement that the group include transformations to or from an inertial to an accelerated frame. Two-parameter groups of two-dimensional (1 + 1), three-dimensional (2 + 1), and four-dimensional (3 + 1) transformations, with the group parameters related to the ratio of accelerations of the frames and the relative velocity of the frame space origins at the initial moment, can be considered as counterparts of the Lorentz group of corresponding dimensions. Defining the form of the interval and the groups of coordinate transformations satisfying the relativity principle paves the way to defining the invariant forms of the laws of dynamics and electrodynamics in accelerated frames. Thus, the problem of extending the relativity principle from inertial to uniformly accelerated frames has been resolved without use of the equivalence principle and/or the general relativity equations. As an application of the transformations to purely kinematic phenomena, the problem of differential aging between accelerated twins is treated. Full article
(This article belongs to the Special Issue Symmetry in Classical and Quantum Gravity and Field Theory)
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12 pages, 407 KiB  
Article
Gravitational Refraction of Compact Objects with Quadrupoles
by Nurzada Beissen, Daniya Utepova, Medeu Abishev, Hernando Quevedo, Manas Khassanov and Saken Toktarbay
Symmetry 2023, 15(3), 614; https://doi.org/10.3390/sym15030614 - 28 Feb 2023
Cited by 9 | Viewed by 2158
Abstract
We use the material medium approach to derive the refractive index that can be associated with the gravitational field of a compact object with a quadrupole moment. We consider both a static deformation and a stationary rotation of the gravitational source as the [...] Read more.
We use the material medium approach to derive the refractive index that can be associated with the gravitational field of a compact object with a quadrupole moment. We consider both a static deformation and a stationary rotation of the gravitational source as the source of the quadrupole. We show that up to the first order in the quadrupole, the refractive indices of both configurations are equivalent such that from the point of view of refraction, a mimicking effect can occur. This also holds at the level of the deflection angle. We argue that it is possible to use the refractive indices and the parameters of the trajectories of light rays that propagate in a gravitational field to determine the physical parameters of the source. Full article
(This article belongs to the Special Issue Symmetry in Classical and Quantum Gravity and Field Theory)
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