Symmetry: Feature Papers 2020

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

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 23716

Special Issue Editor

ICREA, P. Lluis Companyas 23, 08010 Barcelona and Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193 Barcelona, Spain
Interests: cosmology; dark energy and inflation; quantum gravity; modified gravity and beyond general relativity; quantum fields at external fields
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Special Issue Information

Dear Colleagues,

As Editor-in-Chief of the journal Symmetry, I am glad to announce the Special Issue “Symmetry: Feature Papers 2020” online. In past several years, we cooperated with some excellent scholars/scientific groups and published several very important high-level works which have already been cited according to the data of Web of Science. We aim to introduce a new insight into science development or cutting edge technology related to the symmetry field, which will make a great contribution to the community. Thus, we will continue the Special Issue “Symmetry: Feature Papers” series in 2020. We will strictly select 5–10 papers from excellent scholars around the world to publish for free in order to benefit both authors and readers.

You are welcome to send short proposals for submissions of Feature Papers to our Editorial Office ([email protected]) before submission. They will be evaluated by Editors firstly. Please note that selected full papers will still be subjected to a thorough and rigorous peer review.

Prof. Dr. Sergei D. Odintsov
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.

Published Papers (11 papers)

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Editorial

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2 pages, 164 KiB  
Editorial
Editorial for Special Issue Feature Papers 2020
by Sergei D. Odintsov
Symmetry 2023, 15(1), 8; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15010008 - 20 Dec 2022
Cited by 3 | Viewed by 772
Abstract
This issue of featured papers from 2020 is related to the study of symmetry phenomena in various different fields, but mainly in theoretical physics [...] Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)

Research

Jump to: Editorial

103 pages, 5818 KiB  
Article
The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
by Kaushik Y. Bhagat, Baibhab Bose, Sayantan Choudhury, Satyaki Chowdhury, Rathindra N. Das, Saptarshhi G. Dastider, Nitin Gupta, Archana Maji, Gabriel D. Pasquino and Swaraj Paul
Symmetry 2021, 13(1), 44; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010044 - 30 Dec 2020
Cited by 21 | Viewed by 3661
Abstract
The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general [...] Read more.
The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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17 pages, 2465 KiB  
Article
The Cauchy Problem for the Generalized Hyperbolic Novikov–Veselov Equation via the Moutard Symmetries
by Alla A. Yurova, Artyom V. Yurov and Valerian A. Yurov
Symmetry 2020, 12(12), 2113; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122113 - 19 Dec 2020
Cited by 2 | Viewed by 1870
Abstract
We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which [...] Read more.
We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which in turn serves as a solution to the ordinary differential equation d2zdξ2=ξz. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov–Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation dn1zdξn1=ξz. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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18 pages, 314 KiB  
Article
Lagrangian Formulation of Free Arbitrary N-Extended Massless Higher Spin Supermultiplets in 4D AdS Space
by Ioseph L. Buchbinder and Timofey V. Snegirev
Symmetry 2020, 12(12), 2052; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122052 - 10 Dec 2020
Cited by 9 | Viewed by 1393
Abstract
We derived the component Lagrangian for the free N-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction was based on the frame-like description of massless integer and half-integer higher spin fields. The massless supermultiplets were formulated for [...] Read more.
We derived the component Lagrangian for the free N-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction was based on the frame-like description of massless integer and half-integer higher spin fields. The massless supermultiplets were formulated for N4k, where k is a maximal integer or half-integer spin in the multiplet. The supertransformations that leave the Lagrangian invariant were found in explicit form and it was shown that their algebra is closed on-shell. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
13 pages, 323 KiB  
Article
General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach
by Sabit Bekov, Kairat Myrzakulov, Ratbay Myrzakulov and Diego Sáez-Chillón Gómez
Symmetry 2020, 12(12), 1958; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12121958 - 26 Nov 2020
Cited by 20 | Viewed by 1911
Abstract
Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms [...] Read more.
Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
30 pages, 391 KiB  
Article
Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces
by Alexander Breev and Alexander Shapovalov
Symmetry 2020, 12(11), 1867; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111867 - 13 Nov 2020
Cited by 18 | Viewed by 1499
Abstract
We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us [...] Read more.
We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
43 pages, 1117 KiB  
Article
Antisymmetric Tensor Fields in Modified Gravity: A Summary
by Tanmoy Paul
Symmetry 2020, 12(9), 1573; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091573 - 22 Sep 2020
Cited by 9 | Viewed by 2495
Abstract
We provide various aspects of second rank antisymmetric Kalb–Ramond (KR) field in modified theories of gravity. The KR field energy density is found to decrease with the expansion of our universe at a faster rate in comparison to radiation and matter components. Thus [...] Read more.
We provide various aspects of second rank antisymmetric Kalb–Ramond (KR) field in modified theories of gravity. The KR field energy density is found to decrease with the expansion of our universe at a faster rate in comparison to radiation and matter components. Thus as the universe evolves and cools down, the contribution of the KR field on the evolutionary process reduces significantly, and at present it almost does not affect the universe evolution. However the KR field has a significant contribution during early universe; in particular, it affects the beginning of inflation as well as increases the amount of primordial gravitational radiation and hence enlarges the value of tensor-to-scalar ratio in respect to the case when the KR field is absent. In regard to the KR field couplings, it turns out that in four dimensional higher curvature inflationary model the couplings of the KR field to other matter fields is given by 1/MPl (where MPl is known as the “reduced Planck mass” defined by MPl=18πG with G is the “Newton’s constant”) i.e., same as the usual gravity–matter coupling; however in the context of higher dimensional higher curvature model the KR couplings get an additional suppression over 1/MPl. Thus in comparison to the four dimensional model, the higher curvature braneworld scenario gives a better explanation of why the present universe carries practically no footprint of the Kalb–Ramond field. The higher curvature term in the higher dimensional gravitational action acts as a suitable stabilizing agent in the dynamical stabilization mechanism of the extra dimensional modulus field from the perspective of effective on-brane theory. Based on the evolution of KR field, one intriguing question can be—“sitting in present day universe, how do we confirm the existence of the Kalb–Ramond field which has considerably low energy density (with respect to the other components) in our present universe but has a significant impact during early universe?” We try to answer this question by the phenomena “cosmological quantum entanglement” which indeed carries the information of early universe. Finally, we briefly discuss some future perspectives of Kalb–Ramond cosmology at the end of the paper. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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16 pages, 285 KiB  
Article
Shapovalov Wave-Like Spacetimes
by Konstantin Osetrin and Evgeny Osetrin
Symmetry 2020, 12(8), 1372; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081372 - 18 Aug 2020
Cited by 22 | Viewed by 1755
Abstract
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric [...] Read more.
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
15 pages, 287 KiB  
Article
Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)
by Valeriy Obukhov
Symmetry 2020, 12(8), 1289; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081289 - 03 Aug 2020
Cited by 19 | Viewed by 2395
Abstract
All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as [...] Read more.
All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
18 pages, 991 KiB  
Article
Unified Inflation and Late-Time Accelerated Expansion with Exponential and R2 Corrections in Modified Gravity
by Luis Granda
Symmetry 2020, 12(5), 794; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050794 - 09 May 2020
Cited by 10 | Viewed by 1990
Abstract
Modified gravity models with and exponential function of curvature and R 2 corrections are proposed. At low curvature, the model explains the matter epoch and the late time accelerated expansion while at the inflation epoch the leading term is R 2 . At [...] Read more.
Modified gravity models with and exponential function of curvature and R 2 corrections are proposed. At low curvature, the model explains the matter epoch and the late time accelerated expansion while at the inflation epoch the leading term is R 2 . At R 0 the cosmological constant disappears, giving unified description of inflation and dark energy in pure geometrical context. The models satisfy the stability conditions, pass local tests and are viable in the ( r , m ) -plane, where the trajectories connect the saddle matter dominated critical point ( r = 1 , m = 0 ) with the late time de Sitter attractor at r = 2 and 0 < m 1 . Initial conditions were found, showing that the density parameters evolve in a way consistent with current cosmological observations, predicting late time behavior very close to the Λ CDM with future universe evolving towards the de Sitter attractor. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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9 pages, 1637 KiB  
Article
Chiral Dualism as an Instrument of Hierarchical Structure Formation in Molecular Biology
by Vsevolod A. Tverdislov and Ekaterina V. Malyshko
Symmetry 2020, 12(4), 587; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12040587 - 08 Apr 2020
Cited by 24 | Viewed by 3016
Abstract
The origin of chiral asymmetry in biology has attracted the attention of the research community throughout the years. In this paper we discuss the role of chirality and chirality sign alternation (L–D–L–D in proteins and D–L–D–L in DNA) in promoting self-organization in biology, [...] Read more.
The origin of chiral asymmetry in biology has attracted the attention of the research community throughout the years. In this paper we discuss the role of chirality and chirality sign alternation (L–D–L–D in proteins and D–L–D–L in DNA) in promoting self-organization in biology, starting at the level of single molecules and continuing to the level of supramolecular assemblies. In addition, we also discuss chiral assemblies in solutions of homochiral organic molecules. Sign-alternating chiral hierarchies created by proteins and nucleic acids are suggested to create the structural basis for the existence of selected mechanical degrees of freedom required for conformational dynamics in enzymes and macromolecular machines. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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