Working Paper Article Version 1 This version is not peer-reviewed

Supersymmetry of Relativistic Hamiltonians for Arbitray Spin

Version 1 : Received: 16 August 2020 / Approved: 19 August 2020 / Online: 19 August 2020 (10:47:38 CEST)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Symmetry 2020, 12, 1590
DOI: 10.3390/sym12101590

Abstract

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

Subject Areas

Relativistic Wave Equation; Klein-Gordan Equation; Dirac Equation; Proca Equation; Supersymmetry

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