Supersymmetry, Foldy-Wouthuysen transformations, and relativistic oscillators

Abstract

Dirac Hamiltonians expressed in terms of supercharges are analyzed in connection with supersymmetric quantum mechanics. Unitary Foldy-Wouthuysen transformations lead to equivalent diagonalized Hamiltonians, functions of supersymmetric (nonrelativistic) ones. Such considerations permit the definition of relativistic oscillators described by Dirac equations.