Supersymmetric quantum mechanics in a first-order Dirac equation

Abstract

We demonstrate the realization of supersymmetric quantum mechanics in the standard first-order Dirac equation describing a massless Dirac particle in a magnetic field. This system is relevant to the integer quantum Hall effect. In obtaining the first-order supersymmetry, square-root operators are used and justified. A detailed discussion is also provided of the simpler problem of supersymmetry in the context of the relativistic Pauli Hamiltonian squared. In addition we discuss a realization of the superalgebra osp(1/2) obtained from this system.