Supersymmetric Dirac Hamiltonians in () dimensions revisited
European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748, Garching, Germany
Accepted: 14 May 2020
Published online: 3 June 2020
The most general Dirac Hamiltonians in dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral properties are shown to be represented by those of the associated non-relativistic Witten model. The general discussion is extended to include the corresponding relativistic and non-relativistic resolvents. As example, the well-studied relativistic Dirac oscillator is considered and the associated resolved kernel is found in a closed-form expression by utilising the energy-dependent Green’s function of the non-relativistic harmonic oscillator. The supersymmetric quasi-classical approximation for the Witten model is extended to the associated relativistic model.
© The Author(s) 2020
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