Spin-Matrix Polynomial Development of the Hamiltonian for a Free Particle of Arbitrary Spin and Mass

Abstract

The Hamiltonian and other relevant physical operators for a free particle of arbitrary spin and mass, based upon the generalized Foldy-Wouthuysen transformation, are developed in terms of the spin-matrix polynomials. The general theory of these polynomials, given in an earlier paper, is reviewed briefly. It is a general feature of these expansions that the number of terms is determined by the spin of the particle, but the coefficients are spin-independent. The massless limit is examined in some detail and the invariant metric operator is discussed.