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32 pages, 419 KiB

Open AccessArticle

Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

by Robert Bluhm and Yu Zhi

Symmetry 2024, 16(1), 25; https://doi.org/10.3390/sym16010025 - 24 Dec 2023

Viewed by 693

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The [...] Read more.

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

31 pages, 667 KiB

Open AccessArticle

Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder

by Jean-Pierre Gazeau and Romain Murenzi

Symmetry 2023, 15(11), 2044; https://doi.org/10.3390/sym15112044 - 10 Nov 2023

Viewed by 1182

Abstract

Covariant integral quantization with rotational

SO (3)

symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The [...] Read more.

Covariant integral quantization with rotational

SO (3)

symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on

SO (3)

. This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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53 pages, 1751 KiB

Open AccessFeature PaperArticle

Generalized Finsler Geometry and the Anisotropic Tearing of Skin

by John D. Clayton

Symmetry 2023, 15(10), 1828; https://doi.org/10.3390/sym15101828 - 26 Sep 2023

Cited by 1 | Viewed by 816

Abstract

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal [...] Read more.

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer’s lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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23 pages, 2812 KiB

Open AccessArticle

d-Idose-Based Monoaza-15-Crown-5 Lariat Ethers: Synthesis of an Elusive d-Hexose and Application of Derived Macrocycles in Enantioselective Syntheses

by István Orbán, Dóra Ujj, Béla Mátravölgyi, Tamás Holczbauer and Zsolt Rapi

Symmetry 2023, 15(9), 1714; https://doi.org/10.3390/sym15091714 - 07 Sep 2023

Viewed by 805

Abstract

Carbohydrate-based macrocycles can be enantioselective catalysts in certain reactions. Previously, it was proven that the carbohydrate moiety could affect the catalytic activity of the monoaza-15-crown-5 type macrocycles derived from sugars. According to our experiments so far, the most effective enantioselective catalysts were the [...] Read more.

Carbohydrate-based macrocycles can be enantioselective catalysts in certain reactions. Previously, it was proven that the carbohydrate moiety could affect the catalytic activity of the monoaza-15-crown-5 type macrocycles derived from sugars. According to our experiments so far, the most effective enantioselective catalysts were the d-glucose- and the d-galactose-based crown ethers. To obtain more information about the effect of the carbohydrate unit, a rare monosaccharide, d-idose was incorporated into the monoaza-15-crown-5 structure. The key intermediates were methyl 4,6-O-benzylidene-α-d-idopyranoside and methyl 4,6-O-benzylidene-β-d-idopyranoside, which were synthesized from d-galactose. The efficiency of the idopyranoside-based crown compounds synthesized was investigated in asymmetric phase transfer reactions. In liquid-liquid biphasic reactions the highest enantioselectivity was 81% ee, while in solid-liquid phase systems the highest asymmetric induction was 67% ee. It was observed that the enantiodiscrimination was strongly dependent on the configuration of the anomeric center, on the side arm of the nitrogen, and on the structure of the substrate. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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15 pages, 770 KiB

Open AccessArticle

Strong Necessary Conditions and the Cauchy Problem

by Łukasz T. Stȩpień

Symmetry 2023, 15(9), 1622; https://doi.org/10.3390/sym15091622 - 22 Aug 2023

Viewed by 645

Abstract

Some exact solutions of boundary or initial conditions formulated for Bogomolny equations (derived by using the strong necessary conditions and associated with some ordinary equation and some partial differential equations) have been found. The solution obtained for the restricted baby Skyrme model, as [...] Read more.

Some exact solutions of boundary or initial conditions formulated for Bogomolny equations (derived by using the strong necessary conditions and associated with some ordinary equation and some partial differential equations) have been found. The solution obtained for the restricted baby Skyrme model, as well the density of energy for this solution, are localized. Moreover, it turns out that the densities of the ungauged Hamiltonian and the gauged Hamiltonian are correspondingly, non-zero and zero for the found solution of the Cauchy problem associated with the Bogomolny equation of the restricted baby Skyrme model. Hence, a degeneracy of the Hamiltonian for this model has been established. As such, one can see the breaking of some symmetry. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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17 pages, 1470 KiB

Open AccessArticle

Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates

by Kannan Manikandan, Nurzhan Serikbayev, Shunmuganathan P. Vijayasree and Devarasu Aravinthan

Symmetry 2023, 15(8), 1585; https://doi.org/10.3390/sym15081585 - 14 Aug 2023

Viewed by 693

Abstract

In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern [...] Read more.

In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. This study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or sech-like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of captivating behaviors in the matter-wave smooth positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate density profile of matter-wave smooth positons in BECs, providing valuable insights into their controllable behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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24 pages, 333 KiB

Open AccessFeature PaperArticle

Deviation of Geodesics, Particle Trajectories and the Propagation of Radiation in Gravitational Waves in Shapovalov Type III Wave Spacetimes

by Konstantin Osetrin, Evgeny Osetrin and Elena Osetrina

Symmetry 2023, 15(7), 1455; https://doi.org/10.3390/sym15071455 - 21 Jul 2023

Cited by 2 | Viewed by 831

Abstract

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions [...] Read more.

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions are obtained for the equations of geodesic deviation and tidal acceleration of particles in a gravitational wave in privileged coordinate systems. An explicit analytical law of transition from a privileged coordinate system to a synchronous reference system associated with a freely falling observer with an explicit selection of time and spatial coordinates is obtained. An explicit form of the metric of a gravitational wave in a synchronous frame of reference is obtained. For a synchronous frame of reference, the trajectories of particles and radiation, the deviation of geodesics, and tidal accelerations in a gravitational wave are obtained. The presented methods and approaches are applicable both to Einstein’s general theory of relativity and to modified theories of gravity. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

31 pages, 1225 KiB

Open AccessFeature PaperArticle

A Study on the Various Aspects of Bounce Realisation for Some Choices of Scale Factors

by Sanghati Saha, Ertan Güdekli and Surajit Chattopadhyay

Symmetry 2023, 15(7), 1332; https://doi.org/10.3390/sym15071332 - 29 Jun 2023

Cited by 1 | Viewed by 1320

Abstract

The current study examines the realisation of cosmic bounce in two situations involving two distinct scale factor selections, one of which is a scale factor already developed for bouncing and the other of which is a scale factor created by truncating a series [...] Read more.

The current study examines the realisation of cosmic bounce in two situations involving two distinct scale factor selections, one of which is a scale factor already developed for bouncing and the other of which is a scale factor created by truncating a series expansion of a de Sitter scale factor. Generalized Chaplygin gas (GCG) is assumed to be the background fluid in both situations. When the scale factor is set to the first kind, the pre-bounce scenario’s GCG energy density decreases due to contraction, reaches its lowest point at

t = 0

during the bounce, and then rises as a result of expansion following the bounce. However, it is noted that the truncation has an impact on the density evolution from pre-bounce in the other scale factor scenario. The influence of bulk viscosity is shown in all circumstances, in addition to the influence of non-viscosity, and the test for stability makes use of the squared speed of sound. At the turn-around places, the null energy criterion is also violated. The final stage of the study includes a cosmographic analysis and a demonstration of the Hubble flow dynamics. In conclusion, we find that inflationary cosmology can also be realized with GCG as the background fluid for two-scale factor options. When the equivalent cosmic parameter is examined for pre-bounce and post-bounce scenarios, a symmetry is frequently seen. The symmetry occurs near the point of bouncing or turning. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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18 pages, 349 KiB

Open AccessFeature PaperArticle

Gauging Fractons and Linearized Gravity

by Erica Bertolini, Alberto Blasi, Andrea Damonte and Nicola Maggiore

Symmetry 2023, 15(4), 945; https://doi.org/10.3390/sym15040945 - 20 Apr 2023

Cited by 5 | Viewed by 1009

Abstract

We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the [...] Read more.

We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the paradigm that quantum field theories are defined by their symmetries, fractons unavoidably come together with linearized gravity. The standard Faddeev–Popov procedure to gauge fix the theory leads to a scalar gauge condition, which has two important drawbacks: it is frozen in the Landau gauge and linearized gravity cannot be obtained as a limit. In this paper, we adopt a tensorially alternative gauge fixing, which avoids both problems. In particular, this allows to show that important physical features, such as counting of the degrees of freedom, do not depend on a particular gauge choice, as expected. Moreover, the resulting gauge fixed theory contains both fractons and linearized gravity as a limit, differently from the standard scalar choice. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

16 pages, 482 KiB

Open AccessFeature PaperArticle

On Equivalence between Kinetic Equations and Geodesic Equations in Spaces with Affine Connection

by Alexander V. Shapovalov

Symmetry 2023, 15(4), 905; https://doi.org/10.3390/sym15040905 - 13 Apr 2023

Cited by 3 | Viewed by 912

Abstract

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the kinetic equations and the geodesic equations of some affinely connected space

A

associated with the kinetic equation and called the kinetic space of affine connection. The [...] Read more.

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the kinetic equations and the geodesic equations of some affinely connected space

A

associated with the kinetic equation and called the kinetic space of affine connection. The geometric properties of equations are treated locally in some coordinate chart

(x; U)

. The peculiarity of the space

A

is that in the coordinates

(x)

of some selected local chart, the Christoffel symbols defining the affine connection of the space

A

are constant. Examples of the Smoluchowski equation for agglomeration processes without fragmentation and the exchange-driven growth equation are considered for small dimensions in terms of geodesic equations. When fragmentation is taken into account, the kinetic equations can be written as equations of quasigeodesics. Particular cases of spaces with symmetries are discussed. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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12 pages, 282 KiB

Open AccessFeature PaperArticle

Possible Expansion of Blood Vessels by Means of the Electrostrictive Effect

by Iver Brevik

Symmetry 2023, 15(4), 793; https://doi.org/10.3390/sym15040793 - 24 Mar 2023

Cited by 2 | Viewed by 1012

Abstract

In cases when it is desirable to transport medication through blood vessels, especially when dealing with brain cancer being confronted with the narrow arteries in the brain, the blood–brain barrier makes medical treatment difficult. There is a need of expanding the diameters of [...] Read more.

In cases when it is desirable to transport medication through blood vessels, especially when dealing with brain cancer being confronted with the narrow arteries in the brain, the blood–brain barrier makes medical treatment difficult. There is a need of expanding the diameters of the arteries in order to facilitate the transport of medications. Recent research has pointed to various ways to improve this situation; in particular, the use an ultrasound acting on microbubbles in the blood stream has turned out to be a promising option. Here, a different possibility of enlarging the diameters of arteries is discussed, namely to exploit the electrostrictive pressure produced by internal strong, ultrashort and repetitive laser pulses. Each pulse will at first give rise to inward-directed optical forces, and once the pulse terminates, there will be a hydrodynamical bouncing flow in the outward radial direction, giving an outward impulse to the vessel wall. In the absence of friction, a symmetric oscillation picture emerges. Clearly, a supply of repetitive pulses will be needed (at a parametric resonance) to make the effect appreciable. The effect has, to our knowledge, not been discussed before. We give an approximate optical and hydrodynamical theory of it. The calculations indicate promising results for the wall pressure, although experimental work is desirable to demonstrate whether the idea can be useful in practice. Our calculation is made from a general physical perspective that is not necessarily linked to medical applications. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

14 pages, 1363 KiB

Open AccessArticle

Algebraic Morphology of DNA–RNA Transcription and Regulation

by Michel Planat, Marcelo M. Amaral and Klee Irwin

Symmetry 2023, 15(3), 770; https://doi.org/10.3390/sym15030770 - 21 Mar 2023

Cited by 1 | Viewed by 1754

Abstract

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite [...] Read more.

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite group theory and of algebraic geometry to describe both TFs and miRNAs. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group

π

, we compute the

S L (2, C)

character variety, where

S L (2, C)

is simultaneously a ‘space-time’ (a Lorentz group) and a ‘quantum’ (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when

π

looks similar to a free group

F_{r}

(

r = 1

to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non-free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis

G

of the variety. A surface with simple singularities (such as the well known Cayley cubic) within

G

is a signature of a potential disease even when

π

looks similar to a free group

F_{r}

in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in

{A, T / U, G, C}

. We produce a few tables of human TFs and miRNAs showing that a disease may occur when either

π

is away from a free group or

G

contains surfaces with isolated singularities. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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25 pages, 7792 KiB

Open AccessFeature PaperArticle

Optical Channeling of Low Energy Antiprotons in Thin Crystal Targets

by Andrea Bianconi, Giovanni Costantini, Giulia Gosta, Marco Leali, Valerio Mascagna, Stefano Migliorati and Luca Venturelli

Symmetry 2023, 15(3), 724; https://doi.org/10.3390/sym15030724 - 14 Mar 2023

Viewed by 1081

Abstract

A relevant aspect of the interactions between charged fermions and crystal targets is coherence, which can exist at both classical and quantum levels. In the case of antiprotons crossing crystal targets, there are theories and measurements of classical-level coherence effects, in particular, channeling [...] Read more.

A relevant aspect of the interactions between charged fermions and crystal targets is coherence, which can exist at both classical and quantum levels. In the case of antiprotons crossing crystal targets, there are theories and measurements of classical-level coherence effects, in particular, channeling effects. For the present study, we assume the existence of a low-energy regime where the electrostatic interactions between an antiproton and the crystal atoms lead to a local loss in the beam flux as their leading effect. We expect this assumption to be well-justified for antiproton (

\bar{p}

) energies below 100 eV, with a progressive transition to a standard “Rutherford regime” in the energy range 100–1000 eV. Under these conditions, the target can be treated as an optical absorber with a periodical structure, which can be simplified by considering a multi-layer planar structure only. As in standard optics, wave absorption is accompanied by interference and diffraction. Assuming sub-nanometer ranges for the relevant parameters and a realistic angular spread for the antiproton beam, we find narrow-angle focusing effects that reproduce the classical channeling effect at a qualitative level. We also find that diffraction dominates over interference, although this may strongly depend on the target details. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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16 pages, 341 KiB

Open AccessArticle

Gauging the Maxwell Extended

GL (n, R)

and

SL (n + 1, R)

Algebras

by Salih Kibaroğlu, Oktay Cebecioğlu and Ahmet Saban

Symmetry 2023, 15(2), 464; https://doi.org/10.3390/sym15020464 - 09 Feb 2023

Cited by 1 | Viewed by 942

Abstract

We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in D space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie [...] Read more.

We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in D space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a suitable contraction of generalized algebras. The extended Lie algebras could be useful in the construction of generalized gravity theories and the objects that couple to them. We also consider the gravitational dynamics of these algebras in the framework of the gauge theories of gravity. By adopting the symmetry-breaking mechanism of the Stelle–West model, we present some modified gravity models that contain the generalized cosmological constant term in four dimensions. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

Review

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20 pages, 3392 KiB

Open AccessReview

The Supramolecular Matrix Concept

by Oleg Epstein

Symmetry 2023, 15(10), 1914; https://doi.org/10.3390/sym15101914 - 13 Oct 2023

Cited by 2 | Viewed by 1205

Abstract

It has been established that dilutions of a variety of substances, when exposed to vibration in the process of their preparation, acquire not only new structural characteristics in the form of nano-associates but also new physical properties, regardless of the presence of the [...] Read more.

It has been established that dilutions of a variety of substances, when exposed to vibration in the process of their preparation, acquire not only new structural characteristics in the form of nano-associates but also new physical properties, regardless of the presence of the initial substance. One of the most important properties of these dilutions is the ability to modify the physico–chemical and biological activity of the initial substance as well as exert non-contact, “distant”, effects. Here, we propose a novel hypothesis that the basis of modifying activity is the transformation of target molecules to a more harmonious (symmetrical) state supported by a supramolecular matrix, a structural unit of a structured space. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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