The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields

TL;DR

This paper derives solutions to the Dirac equation for particles on a hyperboloid surface under perpendicular magnetic fields, extending from massless to massive cases using supersymmetric quantum mechanics methods.

Contribution

It introduces a method to solve the Dirac equation for both massless and massive particles on a hyperboloid under magnetic fields, expanding previous solutions for the massless case.

Findings

Solutions for massless Dirac particles obtained using SUSY quantum mechanics.

Extended solutions to include massive particles on the hyperboloid.

Explicit example of constant magnetic field case analyzed.

Abstract

In this study, firstly it is reviewed how the solutions of the Dirac-Weyl equation for a massless charge on the hyperboloid under perpendicular magnetic fields are obtained by using supersymmetric (SUSY) quantum mechanics methods. Then, the solutions of the Dirac equation for a massive charge under magnetic fields have been computed in terms of the solutions which were found before for the Dirac-Weyl equation. As an example, the case of a constant magnetic field on the hyperbolic surface for massless and massive charges has been worked out.