Relativistic field equations from higher-order polarizations of the Poincaré group

Abstract

The theory of free relativistic fields is shown to arise in a unified manner from higher-order, configuration-space, irreducible representations of the Poincaré group. A de Sitter subalgebra, in the massive case, and a Poincaré subalgebra, in the massless case, of the enveloping algebra of the Poincaré group are the suitable higher-order polarizations. In particular, a simple group-theoretic derivation of the Dirac equation is given.