On a neutral Dirac particle interacting with a magnetic field in a topological defect space-time and its hidden supersymmetry

In this paper, we study the relativistic quantum dynamics of a neutral Dirac particle with a permanent magnetic dipole moment that interacts with an external magnetic field in the background space-time of a linear topological defect called spiral dislocation. The generalized Dirac wave equation is derived from the full action of that model involving the Lagrangian density of the Dirac spinor field in the background and the interaction model. The energy eigenvalues and corresponding wave functions are found in closed form by reducing the problem to that of a non-relativistic particle moving freely on a plane with a hole at the origin whose radius is determined by the defect parameter. In the limit of vanishing external magnetic field we are also able to establish a hidden SUSY structure of the underlying Dirac Hamiltonian allowing us to discuss the non-relativistic limit in some detail.