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

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.knowledgements M. N. is grateful to the Spanish M.E.C., C.S.I.C. and I.M.A.F.F. for a research contract, and to the Imperial College, where this paper was written, for its boundless hospitality. M. Calixto acknowledges the Spanish M.E.C for a F.P.I. grant. This work was partially supported by the DGICYT.Peer Reviewe