Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin

• URL: http://arxiv.org/abs/2009.02153v1
• Date: Mon, 17 Aug 2020 05:44:35 GMT
• Title: Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin
• Authors: Georg Junker
• Abstract summary: Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure. An exact Foldy-Wouthuysen transformation exits which brings it into a block-diagonal form separating the positive and negative energy subspaces.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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