Relativistic field equations from higher-order polarizations of the Poincar\'e group

TL;DR

This paper demonstrates how free relativistic fields can be derived from higher-order representations of the Poincaré group, providing a unified group-theoretic framework for field equations including Dirac's.

Contribution

It introduces a novel approach using higher-order polarizations of the Poincaré group to derive relativistic field equations in a unified manner.

Findings

Derivation of relativistic field equations from higher-order group representations

Identification of de Sitter and Poincaré subalgebras as polarizations

Group-theoretic derivation of the Dirac equation

Abstract

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