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arXiv · 1911.00454

Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited

Georg Junker
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Abstract

The most general Dirac Hamiltonians in $(1+1)$ 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.

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Georg Junker. 2019-11-01. Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited. https://doi.org/10.1140/epjp%2Fs13360-020-00464-y

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