Generalized covariance principles and neutrino physics

Abstract

The zero-mass Dirac equation admits a simple generalized covariance group which is an inhomogeneous Lorentz group G different from the Poincaré group. Its mathematical structure and unitary irreducible representations have been studied by Flato and Hillion [Phys. Rev. D 1, 1667 (1970)]. Physical consequences concerning neutrino physics were then obtained by introduction of the Stokes parameters. The present article is divided into three parts: (1) Introduction, in which we present briefly the idea of generalized convariance, summarize the main results obtained by Flato and Hillion, and introduce the 14-dimensional unification group proper for the generalized convariance of the free neutrino equation. (2) In the second part, we study by the well-known method of induced representations all the strongly continuous unitary irreducible representations of the 10-dimensional Dirac group G as well as of the 14-dimensional unification group G′. (3) Physical applications: in this chapter, we concentrate on particular zero-mass representations of G′ which are of interest at least for the study of the neutrino free-field theory. These classes of unitary irreducible representations of G′ permit us to have two possible physical alternatives which are discussed.