Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin

Language
en
Document Type
Article
Issue Date
2020-12-30
First published
2020-09-24
Issue Year
2020
Authors
Junker, Georg
Editor
Publisher
MDPI
Abstract

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary but fixed spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. Here, the supercharges transform between energy eigenstates of positive and negative energy. For such supersymmetric Hamiltonians, an exact Foldy–Wouthuysen transformation exists which brings it into a block-diagonal form separating the positive and negative energy subspaces. The relativistic dynamics of a charged particle in a magnetic field are considered for the case of a scalar (spin-zero) boson obeying the Klein–Gordon equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation. In the latter case, supersymmetry implies for the Landé g-factor g=2.

Journal Title
Symmetry
Volume
12
Issue
10
Citation
Symmetry 12.10 (2020). <https://www.mdpi.com/2073-8994/12/10/1590>
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