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Symmetry
Special Issues
Symmetry in Mathematical Physics: History, Advances and Applications
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Symmetry in Mathematical Physics: History, Advances and Applications

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 1304

Special Issue Editors

Prof. Dr. Michael Tsamparlis

E-Mail Website
Guest Editor
Faculty of Physics, Department of Astronomy, Astrophysics and Mechanics, University of Athens, Panepistemiopolis, 157 83 Athens, Greece
Interests: mathematical physics; cosmology; general relativity; conservation laws; lie algebra; fundamental symmetry
Special Issues, Collections and Topics in MDPI journals
Dr. Antonios Mitsopoulos

E-Mail Website
Guest Editor
Faculty of Physics, Department of Astronomy, Astrophysics and Mechanics, University of Athens, Panepistemiopolis, 157 83 Athens, Greece
Interests: special and general relativity; differential geometry; latex abstract; algebra topology; geometric mechanic; logic; quantum field theory

Special Issue Information

Dear Colleagues,

Symmetry was always a key element in human intelligence and has been used through the ages to express the concept of “perfection” and divine initially in the field of metaphysics and in art and later, through Classical Geometry, in to mathematics. The applications in Physics came the second part of the 19th century and reached their apogee in Quantum Mechanics and field theory the beginning of 20th century. This special volume invites all physicists who apply symmetry in their work to contribute so that it will result in a basic reference for the generations to come. It is important that physicists from all branches of Physics shall contribute to this effort. Works describing the initial applications of symmetry in Relativity and Quantum Mechanics, together with recent works and advances in these fields as well as applications with practical value especially in everyday life are most welcome. We hope all of us will help to produce a first-class reference which will stay for long.

Prof. Dr. Michael Tsamparlis
Dr. Antonios Mitsopoulos
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

  • mathematical physics
  • cosmology
  • general relativity
  • conservation laws
  • lie algebra
  • fundamental symmetry

Published Papers (1 paper)

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Research

16 pages, 326 KiB  
Article
Linearization of Second-Order Non-Linear Ordinary Differential Equations: A Geometric Approach
by Michael Tsamparlis
Symmetry 2023, 15(11), 2082; https://doi.org/10.3390/sym15112082 - 18 Nov 2023
Viewed by 785
Abstract
Using the coefficients of a system semilinear cubic in the first derivative second order differential equations one defines a connection in the space of the independent and dependent variables, which is specified modulo two free parameters. In this way, to any such equation [...] Read more.
Using the coefficients of a system semilinear cubic in the first derivative second order differential equations one defines a connection in the space of the independent and dependent variables, which is specified modulo two free parameters. In this way, to any such equation one associates an affine space which is not necessarily Riemannian, that is, a metric is not required. If such a metric exists, then under the Cartan parametrization the geodesic equations of the metric coincide with the system of the considered semilinear equations. In the present work, we consider semilinear cubic in the first derivative second order differential equations whose Lie symmetry algebra is the sl(3,R). The covariant condition for these equations is the vanishing of the curvature tensor. We demonstrate the method in the solution of the Painlevé-Ince equation and in a system of two equations. Because the approach is geometric, the number of equations in the system is not important besides the complication in the calculations. It is shown that it is possible to linearize an equation in this form using a different covariant condition, for example, assuming the space to be of constant non-vanishing curvature. Finally, it is shown that one computes the associated metric to a semilinear cubic in the first derivatives differential equation using the inverse transformation derived from the transformation of the connection. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Physics: History, Advances and Applications)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

  • mathematical physics
  • cosmology
  • general relativity
  • conservation laws
  • lie algebra
  • fundamental symmetry
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