Local Current Operators for Arbitrary Spin Particles

Abstract

Free current operators are constructed for massive particles with arbitrary spin $j$. Such current operators are related to representations of the U(N,N) type groups and are covariant under the (extended) Poincar\'{e} group and charge conjugation, where the charge conjugation operation is defined as an automorphism on U(N,N) elements. The currents are also required to satisfy current conservation, hermiticity, and locality. The condition that the currents be local is shown to be equivalent to certain integral constraints on form factors. These constraints are satisfied by writing the currents in terms of free local spin $j$ fields. It is shown that there are $(2j+1)$ different local currents for a spin $j$ particle, each with an arbitrary form factor, generalizing the Dirac and Pauli currents for spin 1/2 particles. Static properties of the various currents are also given.