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Symmetry
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Physics and Symmetry Section: Review Papers
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Physics and Symmetry Section: Review Papers

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

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 3703

Special Issue Editors

Prof. Dr. Tomohiro Inagaki

E-Mail Website
Guest Editor
1. Information Media Center, Hiroshima University, 1-7-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8521, Japan
2. Core of Research for the Energetic Universe, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Interests: general aspects of computer science; computational science; high-energy physics and quantum fields; symmetry breaking; informatics in education
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Tianjun Li

E-Mail Website
Guest Editor
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
Interests: particle physics; grand unified theory; string phenomenology; cosmology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

As Associate Section Editor-in-Chief for “Physics and Symmetry”, I am happy to announce the latest Special Issue, “Physics and Symmetry Section: Review Papers”. This Special Issue aims to cover recent advances in physical aspects of symmetry. Symmetry is one of the most important and fundamental concepts on the whole physics world. Symmetry of the physical system is related to invariance under transformations. Physical symmetries are mathematically represented by group theory and used to classify physical states, analyze observed data, and construct theoretical models. Additionally, this Special Issue is open to related topics of “Physics and Symmetry”. 

There is a lot of work involved in applying symmetry and symmetry breaking to a variety of physical systems. We would like to call for review papers in physical aspects of symmetry. 

Prof. Dr. Tomohiro Inagaki
Prof. Dr. Tianjun Li
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.

Keywords

  • Symmetry and conservation laws
  • Mathematical representations of physical symmetry
  • Spontaneous symmetry breaking
  • Phase structure of physical systems
  • Phase transition and critical phenomena
  • Anomaly for physical symmetry
  • Quantum deformation of symmetry
  • Spacetime symmetry
  • Gauge symmetry
  • Conformal symmetry
  • Supersymmetry
  • Flavor symmetry
  • CP violation

Published Papers (3 papers)

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Review

31 pages, 9853 KiB  
Review
Research Progress of Topological Quantum Materials: From First-Order to Higher-Order
by Bing Liu and Wenjun Zhang
Symmetry 2023, 15(9), 1651; https://doi.org/10.3390/sym15091651 - 26 Aug 2023
Viewed by 2864
Abstract
The exploration of topologically nontrivial states in condensed matter systems, along with their novel transport properties, has garnered significant research interest. This review aims to provide a comprehensive overview of representative topological phases, starting from the initial proposal of the quantum Hall insulator. [...] Read more.
The exploration of topologically nontrivial states in condensed matter systems, along with their novel transport properties, has garnered significant research interest. This review aims to provide a comprehensive overview of representative topological phases, starting from the initial proposal of the quantum Hall insulator. We begin with a concise introduction, followed by a detailed examination of first-order topological quantum phases, including gapped and gapless systems, encompassing relevant materials and associated phenomena in experiment. Subsequently, we delve into the realm of exotic higher-order topological quantum phases, examining both theoretical propositions and experimental findings. Moreover, we discuss the mechanisms underlying the emergence of higher-order topology, as well as the challenges involved in experimentally verifying materials exhibiting such properties. Finally, we outline future research directions. This review not only systematically surveys various types of topological quantum states, spanning from first-order to higher-order, but also proposes potential approaches for realizing higher-order topological phases, thereby offering guidance for the detection of related quantum phenomena in experiments. Full article
(This article belongs to the Special Issue Physics and Symmetry Section: Review Papers)
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20 pages, 323 KiB  
Review
Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective
by Otto C. W. Kong and Jason Payne
Symmetry 2021, 13(10), 1925; https://doi.org/10.3390/sym13101925 - 13 Oct 2021
Cited by 3 | Viewed by 1154
Abstract
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of [...] Read more.
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes—via the notion of symmetry contractions—a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein’s theory. We begin with the Poincaré symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter. Full article
(This article belongs to the Special Issue Physics and Symmetry Section: Review Papers)
39 pages, 575 KiB  
Review
Graded Medial n-Ary Algebras and Polyadic Tensor Categories
by Steven Duplij
Symmetry 2021, 13(6), 1038; https://doi.org/10.3390/sym13061038 - 09 Jun 2021
Viewed by 1876
Abstract
Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε-commutativity), we introduce almost mediality (“commutativity-to-mediality” ansatz). Higher graded twisted products and “deforming” [...] Read more.
Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε-commutativity), we introduce almost mediality (“commutativity-to-mediality” ansatz). Higher graded twisted products and “deforming” brackets (being the medial analog of Lie brackets) are defined. Toyoda’s theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. A polyadic (non-strict) tensor category has an n-ary tensor product as an additional multiplication with n−1 associators of the arity 2n−1 satisfying a n2+1-gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called groupal) is defined: they are close to monoidal categories but may not contain units: instead the querfunctor and (natural) functorial isomorphisms, the quertors, are considered (by analogy with the querelements in n-ary groups). The arity-nonreducible n-ary braiding is introduced and the equation for it is derived, which for n=2 coincides with the Yang–Baxter equation. Then, analogously to the first part of the paper, we introduce “medialing” instead of braiding and construct “medialed” polyadic tensor categories. Full article
(This article belongs to the Special Issue Physics and Symmetry Section: Review Papers)
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