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Symmetry
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Supersymmetry Approaches in Quantum Mechanics and Field Theory
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Supersymmetry Approaches in Quantum Mechanics and Field Theory

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

Deadline for manuscript submissions: 28 February 2026 | Viewed by 1839

Special Issue Editor

Dr. Ronaldo Thibes

E-Mail Website
Guest Editor
Department of Exact and Natural Sciences, Universidade Estadual do Sudoeste da Bahia, Candeias 45083-900, BA, Brazil
Interests: hamiltonian function; quantum field theory; quantum symmetries
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The interaction between theoretical physicists and highly specialized mathematician communities is currently experiencing hectic and fast development based on the key recent findings in supersymmetry, connecting mathematical physics, quantum mechanics and quantum field theory in their broadest senses. Since the first generalizations of the harmonic oscillator algebraic method and first studies on the existence of supersymmetric particles in nature, the idea of supersymmetry has come a long way through a very prosperous journey. New recent results on shape invariance, isospectrality, symplectic geometry, Wigner–Dunkl quantum mechanics, dualities and novel symmetries represent lively trending aspects of supersymmetric quantum mechanics with fairly significant applications in many previously unrelated branches within quantum field theory, string theory and statistical physics, not to mention technological applications. In this Special Issue, we focus on hidden and explicit symmetries with corresponding subtleties related to inter-relations between those subjects, leading to important applications for enhancing human knowledge about our world. It is a pleasure to live in such scientifically innovative times.

Dr. Ronaldo Thibes
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.

Keywords

  • susyqm
  • supersymmetry
  • supersymmetric Wigner–Dunkl quantum mechanics
  • isospectrality
  • shape invariance
  • algebraic methods in quantum mechanics
  • factorization method

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Published Papers (2 papers)

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Research

14 pages, 255 KB  
Article
The Retention of Information in the Presence of Increasing Entropy Using Lie Algebras Defines Fibonacci-Type Sequences
by Joseph E. Johnson
Symmetry 2025, 17(9), 1454; https://doi.org/10.3390/sym17091454 - 4 Sep 2025
Viewed by 407
Abstract
In the general linear Lie algebra of continuous linear transformations in n dimensions, we show that unequal Abelian scaling transformations on the components of a vector can stabilize the system information in the presence of Markov component transformations on the vector, which, alone, [...] Read more.
In the general linear Lie algebra of continuous linear transformations in n dimensions, we show that unequal Abelian scaling transformations on the components of a vector can stabilize the system information in the presence of Markov component transformations on the vector, which, alone, would lead to increasing entropy. The more interesting results follow from seeking Diophantine (integer) solutions, with the result that the system can be stabilized with constant information for each of a set of entropy rates (k=1,2,3,… ). The first of these—the simplest—where k=1, results in the Fibonacci sequence, with information determined by the olden mean, and Fibonacci interpolating functions. Other interesting results include the fact that a new set of higher order generalized Fibonacci sequences, functions, golden means, and geometric patterns emerges for k=2, 3, … Specifically, we define the kth order golden mean as Φk=k/2+(k/2)2+1 for k =1, 2, 3, ….. One can easily observe that one can form a right triangle with sides of 1 and k/2 and that this will give a hypotenuse of (k/2)2+1. Thus, the sum of the k/2 side plus the hypotenuse of these triangles so proportioned will give geometrically the exact value of the golden means for any value of k relative to the third side with a value of unity. The sequential powers of the matrix (k2+1,k,k,1) for any integer value of k provide a generalized Fibonacci sequence. Also, using the general equation expressed as Φk=k2+(k/2)2+1 for k =1,2,3, …, one can easily prove that Φk=k+1/Φk which is a generalization of the familiar equation expressed as Φ=1+1/Φ. We suggest that one could look for these new ratios and patterns in nature, with the possibility that all of these systems are connected with the retention of information in the presence of increasing entropy. Thus, we show that two components of the general linear Lie algebra (GL(n,R)), acting simultaneously with certain parameters, can stabilize the information content of a vector over time. Full article
(This article belongs to the Special Issue Supersymmetry Approaches in Quantum Mechanics and Field Theory)
29 pages, 349 KB  
Article
Spin-2 Particle in Coulomb Field: Non-Relativistic Approximation
by Alina Ivashkevich, Viktor Red’kov and Artur Ishkhanyan
Symmetry 2025, 17(7), 1075; https://doi.org/10.3390/sym17071075 - 6 Jul 2025
Viewed by 987
Abstract
The primary objective of this paper is to derive a non-relativistic system of equations for a spin-2 particle in the presence of an external Coulomb field, solve these equations, and determine the corresponding energy spectra. We begin with the known radial system of [...] Read more.
The primary objective of this paper is to derive a non-relativistic system of equations for a spin-2 particle in the presence of an external Coulomb field, solve these equations, and determine the corresponding energy spectra. We begin with the known radial system of 39 equations formulated for a free spin-2 particle and modify it to incorporate the effects of the Coulomb field. By eliminating the 28 components associated with vector and rank-3 tensor fields, we reduce the system to a set of 11 second-order equations related to scalar and symmetric tensor components. In accordance with parity constraints, this system naturally groups into two subsystems consisting of three and eight equations, respectively. To perform the non-relativistic approximation, we employ the method of projective operators constructed from the matrix Γ0 of the original matrix equation. This approach allows us to derive two non-relativistic subsystems corresponding to the parity restrictions, comprising two and three coupled differential equations. Through a linear similarity transformation, we further decouple these into five independent equations with a Schrödinger-type non-relativistic structure, leading to explicit energy spectra. Special attention is given to the case of the minimal quantum number of total angular momentum, j=0, which requires separate consideration. Full article
(This article belongs to the Special Issue Supersymmetry Approaches in Quantum Mechanics and Field Theory)
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