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

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.

11 pages, substantially revised and enlarged

References in corpus (2)

• Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
• Topological transport in Dirac electronic systems: A concise review

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