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BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry:...
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BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary)

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 7925

Special Issue Editors

Prof. Dr. Laszlo Jenkovszky

E-Mail Website
Guest Editor
Bogolyubov Institute for Theoretical Physics Nasu, Kyiv, Ukraine
Interests: high-energy nuclear and particle physics; astroparticle physics
Special Issues, Collections and Topics in MDPI journals
Dr. Matthew J. Lake

E-Mail Website
Guest Editor
1. National Astronomical Research Institute of Thailand, Chiang Mai 50180, Thailand
2. Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Interests: quantum gravity; quantum foundations; quantum information theory; high energy physics; astrophysics; cosmology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to the 190th anniversary of János Bolyai’s “Appendix” and to remembering his stay in Lviv 190 years ago (1831-1832).

Topics:

  • Non-Euclidean geometry in physics (quantum field theory, relativity, astroparticle physics, cosmology, gravitational waves, dark matter, dark energy);
  • Non-Euclidean geometry in mathematics (quantum fields in curved spaces, symmetries and supersymmetry, quantum groups and algebras, integrable systems).

We cordially invite researchers working in these fields to contribute original research papers or review articles to this Special Issue of MDPI’s SCIE-ranked journal Symmetry.

Prof. Dr. Laszlo Jenkovszky
Dr. Matthew J. Lake
Guest Editors

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.

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Published Papers (7 papers)

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Editorial

Jump to: Research

7 pages, 267 KiB  
Editorial
János Bolyai, Carl Friedrich Gauss, Nikolai Lobachevsky and the New Geometry: Foreword
by László Jenkovszky, Matthew J. Lake and Vladimir Soloviev
Symmetry 2023, 15(3), 707; https://doi.org/10.3390/sym15030707 - 12 Mar 2023
Viewed by 3189
Abstract
Nearly 2300 years ago, the Greek mathematician Euclid of Alexandria laid down the basis of the geometry now known from the textbooks and used in everyday life [...] Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
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Research

Jump to: Editorial

9 pages, 342 KiB  
Article
Vacuum Polarization of a Quantized Scalar Field in the Thermal State on the Short Throat Wormhole Background
by Dmitriy Lisenkov and Arkady Popov
Symmetry 2023, 15(2), 426; https://doi.org/10.3390/sym15020426 - 6 Feb 2023
Viewed by 1052
Abstract
Vacuum polarization of a scalar field on the short throat wormhole background is investigated. The scalar field is assumed to be massless, having an arbitrary coupling to the scalar curvature of spacetime. In addition, it is supposed that the field is in a [...] Read more.
Vacuum polarization of a scalar field on the short throat wormhole background is investigated. The scalar field is assumed to be massless, having an arbitrary coupling to the scalar curvature of spacetime. In addition, it is supposed that the field is in a thermal state with an arbitrary temperature. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
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9 pages, 266 KiB  
Article
Theory of Quantum Mechanical Scattering in Hyperbolic Space
by L. L. Jenkovszky, Y. A. Kurochkin, V. S. Otchik, P. F. Pista, N. D. Shaikovskaya and D. V. Shoukavy
Symmetry 2023, 15(2), 377; https://doi.org/10.3390/sym15020377 - 31 Jan 2023
Viewed by 1488
Abstract
The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in [...] Read more.
The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in describing low-energy nuclear interactions is introduced. It is shown that, in the limit of the flat space, i.e., when ρ→∞, the obtained expressions for quantum mechanical scattering in hyperbolic space transform to corresponding formulas in three-dimensional Euclidean space. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
19 pages, 352 KiB  
Article
Klein-Gordon Theory in Noncommutative Phase Space
by Shi-Dong Liang
Symmetry 2023, 15(2), 367; https://doi.org/10.3390/sym15020367 - 30 Jan 2023
Cited by 5 | Viewed by 1705
Abstract
We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the noncommutative parameters associated with the Planck constant, Planck [...] Read more.
We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the noncommutative parameters associated with the Planck constant, Planck length and cosmological constant. As an analog with the electromagnetic gauge potential, the noncommutative effect can be interpreted as an effective gauge field, which depends on the Plank constant and cosmological constant. Based on these noncommutative relations, we give the Klein-Gordon (KG) equation and its corresponding current continuity equation in the noncommutative phase space including the canonical and Hamiltonian forms and their novel properties beyond the conventional KG equation. We analyze the symmetries of the KG equations and some observables such as velocity and force of free particles in the noncommutative phase space. We give the perturbation solution of the KG equation. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
23 pages, 1063 KiB  
Article
Jacobi and Lyapunov Stability Analysis of Circular Geodesics around a Spherically Symmetric Dilaton Black Hole
by Cristina Blaga, Paul Blaga and Tiberiu Harko
Symmetry 2023, 15(2), 329; https://doi.org/10.3390/sym15020329 - 24 Jan 2023
Cited by 5 | Viewed by 1793
Abstract
We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the [...] Read more.
We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potential of the geodesic motion. The Lyapunov stability analysis leads to the same results. Hence, we can conclude that, in the particular case of the geodesic motion on circular orbits in the Gibbons–Maeda–Garfinkle–Horowitz–Strominger, the Lyapunov and the Jacobi stability analysis gives equivalent results. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
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10 pages, 282 KiB  
Article
Quantum Geometry of Spacetime and Quantum Equilibrium
by Yuri Shtanov
Symmetry 2023, 15(1), 227; https://doi.org/10.3390/sym15010227 - 13 Jan 2023
Cited by 1 | Viewed by 1751
Abstract
We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focus on the [...] Read more.
We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focus on the ergodic approach to its resolution. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
13 pages, 295 KiB  
Article
Geodesic (in) Completeness in General Metric Frames
by Valery A. Rubakov and Christof Wetterich
Symmetry 2022, 14(12), 2557; https://doi.org/10.3390/sym14122557 - 3 Dec 2022
Cited by 6 | Viewed by 1408
Abstract
The geometric concept of geodesic completeness depends on the choice of the metric field or “metric frame”. We develop a frame-invariant concept of “generalised geodesic completeness” or “time completeness”. It is based on the notion of physical time defined by counting oscillations for [...] Read more.
The geometric concept of geodesic completeness depends on the choice of the metric field or “metric frame”. We develop a frame-invariant concept of “generalised geodesic completeness” or “time completeness”. It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave functions for particles with varying mass permit the derivation of generalised geodesics and the associated notion of completeness. Time completeness involves aspects of particle physics and is no longer a purely geometric concept. Full article
(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))
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