Massless Particles and Fields

Abstract

Free fields of massless particles transforming covariantly under the Poincaré group are constructed. The allowed infinite- and finite-dimensional representations of the Lorentz group are obtained. The wave functions are calculated in these representations in various bases. The commutation rules are computed, and turn out to be nonlocal for any infinite-dimensional fields. The transformation law of a certain irreducible infinite-dimensional representation is shown to coincide, for its lowest-spin component, with the usual, radiation-gauge, vector-potential transformation law, as already discovered by Bender.