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2 pages, 158 KiB

Open AccessEditorial

Editorial for Feature Papers 2021–2022

by Sergei D. Odintsov

Symmetry 2023, 15(1), 32; https://doi.org/10.3390/sym15010032 - 22 Dec 2022

Cited by 5 | Viewed by 934

Abstract

This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...] Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

Research

Jump to: Editorial

8 pages, 255 KiB

Open AccessArticle

Singular Behavior of the Dark Universe under the Effect of Thermal Radiation in Curved Spacetime

by Iver Brevik and Alexander V. Timoshkin

Symmetry 2023, 15(2), 257; https://doi.org/10.3390/sym15020257 - 17 Jan 2023

Cited by 3 | Viewed by 1226

Abstract

We consider the late-time accelerated universe in the Friedmann–Robertson–Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects [...] Read more.

We consider the late-time accelerated universe in the Friedmann–Robertson–Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects caused by Hawking radiation on the formation of singularities of various classified types, within a finite time. It is shown that under the influence of Hawking radiation, the time of formulation of a singularity and the nature of the singularity itself can change. It is also shown that by jointly taking into account radiation, viscosity, and space curvature, one can obtain a singularity-free universe. The symmetry properties of this kind of theory lie in the assumption about spatial isotropy. The spatial isotropy is also reflected in our use of a bulk instead of a shear viscosity. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

10 pages, 1137 KiB

Open AccessArticle

Dipole-like Field Configurations in Nonperturbative Vacuum

by Vladimir Dzhunushaliev and Vladimir Folomeev

Symmetry 2022, 14(12), 2659; https://doi.org/10.3390/sym14122659 - 15 Dec 2022

Cited by 1 | Viewed by 1176

Abstract

A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations [...] Read more.

A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations existing in this theory. Using an assumption of the behavior of the number density of dipole-like field configurations whose energy approaches infinity, we derive an approximate expression for the energy density of such nonperturbative vacuum symmetrical under translation that turns out to be finite, unlike the infinite energy density of perturbative vacuum. Using characteristic values of the parameters appearing in the expression for the nonperturbative energy density, it is shown that this density may be of the order of the energy density associated with Einstein’s cosmological constant. The physical interpretation of the spinor field self-coupling constant as a characteristic distance between dipole-like field configurations is suggested. The questions of experimental verification of the nonperturbative vacuum model under consideration and of determining its pressure are briefly discussed. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

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20 pages, 472 KiB

Open AccessArticle

Family of Asymptotic Solutions to the Two-Dimensional Kinetic Equation with a Nonlocal Cubic Nonlinearity

by Alexander V. Shapovalov, Anton E. Kulagin and Sergei A. Siniukov

Symmetry 2022, 14(3), 577; https://doi.org/10.3390/sym14030577 - 15 Mar 2022

Cited by 4 | Viewed by 1552

Abstract

We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system of moments of the desired solution to the [...] Read more.

We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system of moments of the desired solution to the kinetic equation and the associated linear partial differential equation. The family of asymptotic solutions to the kinetic equation is constructed using the symmetry operators acting on functions concentrated in a neighborhood of a point determined by the dynamical system. Based on these solutions, we introduce the nonlinear superposition principle for the nonlinear kinetic equation. Our formalism based on the Maslov germ method is applied to the Cauchy problem for the specific two-dimensional kinetic equation. The evolution of the ion distribution in the kinetically enhanced metal vapor active medium is obtained as the nonlinear superposition using the numerical–analytical calculations. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

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18 pages, 279 KiB

Open AccessArticle

Algebra of the Symmetry Operators of the Klein–Gordon–Fock Equation for the Case When Groups of Motions G₃ Act Transitively on Null Subsurfaces of Spacetime

by Valeriy V. Obukhov

Symmetry 2022, 14(2), 346; https://doi.org/10.3390/sym14020346 - 9 Feb 2022

Cited by 19 | Viewed by 1688

Abstract

The algebras of the symmetry operators for the Hamilton–Jacobi and Klein–Gordon–Fock equations are found for a charged test particle, moving in an external electromagnetic field in a spacetime manifold on the isotropic (null) hypersurface, of which a three-parameter groups of motions acts transitively. [...] Read more.

The algebras of the symmetry operators for the Hamilton–Jacobi and Klein–Gordon–Fock equations are found for a charged test particle, moving in an external electromagnetic field in a spacetime manifold on the isotropic (null) hypersurface, of which a three-parameter groups of motions acts transitively. We have found all admissible electromagnetic fields for which such algebras exist. We have proved that an admissible field does not deform the algebra of symmetry operators for the free Hamilton–Jacobi and Klein–Gordon–Fock equations. The results complete the classification of admissible electromagnetic fields, in which the Hamilton–Jacobi and Klein–Gordon–Fock equations admit algebras of motion integrals that are isomorphic to the algebras of operators of the r-parametric groups of motions of spacetime manifolds if

(r \leq 4)

. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

15 pages, 313 KiB

Open AccessArticle

On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation

by Artyom V. Yurov and Valerian A. Yurov

Symmetry 2021, 13(11), 2095; https://doi.org/10.3390/sym13112095 - 5 Nov 2021

Cited by 1 | Viewed by 1608

Abstract

We demonstrate the way to derive the second Painlevé equation

P_{2}

and its Bäcklund transformations from the deformations of the Nonlinear Schrödinger equation (NLS), all the while preserving the strict invariance with respect to the Schlesinger transformations. The proposed algorithm allows for [...] Read more.

We demonstrate the way to derive the second Painlevé equation

P_{2}

and its Bäcklund transformations from the deformations of the Nonlinear Schrödinger equation (NLS), all the while preserving the strict invariance with respect to the Schlesinger transformations. The proposed algorithm allows for a construction of Jordan algebra-based completely integrable multiple-field generalizations of

P_{2}

while also producing the corresponding Bäcklund transformations. We suggest calling such models the JP-systems. For example, a Jordan algebra

J_{_{Mat (N, N)}}

with the Jordan product in the form of a semi-anticommutator is shown to generate an integrable matrix generalization of

P_{2}

, whereas the

V_{_{N}}

algebra produces a different JP-system that serves as a generalization of the Sokolov’s form of a vectorial NLS. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

19 pages, 323 KiB

Open AccessArticle

Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field

by Konstantin Osetrin, Ilya Kirnos, Evgeny Osetrin and Altair Filippov

Symmetry 2021, 13(7), 1173; https://doi.org/10.3390/sym13071173 - 29 Jun 2021

Cited by 9 | Viewed by 1518

Abstract

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of [...] Read more.

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves). Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

21 pages, 325 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Different Faces of Generalized Holographic Dark Energy

by Shin’ichi Nojiri, Sergei D. Odintsov and Tanmoy Paul

Symmetry 2021, 13(6), 928; https://doi.org/10.3390/sym13060928 - 23 May 2021

Cited by 121 | Viewed by 3628

Abstract

In the formalism of generalized holographic dark energy (HDE), the holographic cut-off is generalized to depend upon [...] Read more.

In the formalism of generalized holographic dark energy (HDE), the holographic cut-off is generalized to depend upon

L_{IR} = L_{IR} (L_{p}, {\dot{L}}_{p}, {\ddot{L}}_{p}, \dots, L_{f}, {\dot{L}}_{f}, \dots, a)

with

L_{p}

and

L_{f}

being the particle horizon and the future horizon, respectively (moreover, a is the scale factor of the Universe). Based on such formalism, in the present paper, we show that a wide class of dark energy (DE) models can be regarded as different candidates for the generalized HDE family, with respective cut-offs. This can be thought as a symmetry between the generalized HDE and different DE models. In this regard, we considered several entropic dark energy models—such as the Tsallis entropic DE, the Rényi entropic DE, and the Sharma–Mittal entropic DE—and found that they are indeed equivalent with the generalized HDE. Such equivalence between the entropic DE and the generalized HDE is extended to the scenario where the respective exponents of the entropy functions are allowed to vary with the expansion of the Universe. Besides the entropic DE models, the correspondence with the generalized HDE was also established for the quintessence and for the Ricci DE model. In all the above cases, the effective equation of state (EoS) parameter corresponding to the holographic energy density was determined, by which the equivalence of various DE models with the respective generalized HDE models was further confirmed. The equivalent holographic cut-offs were determined by two ways: (1) in terms of the particle horizon and its derivatives, (2) in terms of the future horizon horizon and its derivatives. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

15 pages, 772 KiB

Open AccessEditor’s ChoiceArticle

Algebra of Symmetry Operators for Klein-Gordon-Fock Equation

by Valeriy V. Obukhov

Symmetry 2021, 13(4), 727; https://doi.org/10.3390/sym13040727 - 20 Apr 2021

Cited by 25 | Viewed by 2415

Abstract

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time

V_{4}

a group of motion

G_{3}

acts simply transitively on a non-null subspace of transitivity

V_{3}

. It is [...] Read more.

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time

V_{4}

a group of motion

G_{3}

acts simply transitively on a non-null subspace of transitivity

V_{3}

. It is shown that in the case of a Riemannian space

V_{n}

, in which the group

G_{r}

acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group

G_{r}

. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

11 pages, 2375 KiB

Open AccessArticle

Linear Energy Density and the Flux of an Electric Field in Proca Tubes

by Vladimir Dzhunushaliev, Vladimir Folomeev and Abylaikhan Tlemisov

Symmetry 2021, 13(4), 640; https://doi.org/10.3390/sym13040640 - 10 Apr 2021

Cited by 5 | Viewed by 1585

Abstract

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the [...] Read more.

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

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15 pages, 1262 KiB

Open AccessEditor’s ChoiceArticle

Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off

by Gargee Chakraborty, Surajit Chattopadhyay, Ertan Güdekli and Irina Radinschi

Symmetry 2021, 13(4), 562; https://doi.org/10.3390/sym13040562 - 29 Mar 2021

Cited by 41 | Viewed by 4724

Abstract

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking [...] Read more.

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to

- 1

for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to

Λ

CDM and cannot go beyond it. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2022)

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