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Open AccessArticle

Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin

by Georg Junker 1,2
1
European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching, Germany
2
Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstraße 7, D-91058 Erlangen, Germany
Symmetry 2020, 12(10), 1590; https://doi.org/10.3390/sym12101590
Received: 16 August 2020 / Revised: 18 September 2020 / Accepted: 22 September 2020 / Published: 24 September 2020
(This article belongs to the Special Issue Symmetries in Quantum Mechanics and Statistical Physics)
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. View Full-Text
Keywords: relativistic wave equation; Klein–Gordon equation; Dirac equation; Proca equation; supersymmetry relativistic wave equation; Klein–Gordon equation; Dirac equation; Proca equation; supersymmetry
MDPI and ACS Style

Junker, G. Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin. Symmetry 2020, 12, 1590.

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