Existence of Degenerate Zero-Energy Ground States of the Dirac Hamiltonian for a Spin 1/2 Neutral Particle with an Anomalous Magnetic Moment in an Arbitrary Dimensional Electrostatic Field

Abstract

It is proven that the Dirac HamiltonianHfor a spin 1/2 neutral particle with an anomalous magnetic moment in an arbitrary dimensional electrostatic field has supersymmetric quantum mechanical structure. By estimating the number of the zero-energy ground states ofHfrom below, it is proven that the ground states are degenerate. The estimate is stated in terms of the order of the scalar potential at infinity. In particular, under suitable conditions, existence of infinitely degenerate zero-energy ground states ofHis proven.