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 912

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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
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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

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Keywords

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

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Published Papers (1 paper)

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Research

29 pages, 349 KiB  
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 622
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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