Covariant representations in a fibre bundle framework

Abstract

Canonical and covariant representations of Lie groups of the semidirect product form G = N⊙ K with N Abelian, are analyzed in a fibre bundle framework. We exhibit first the relationship between both kinds of representations in such framework. Two complementary methods of selecting irreducible representations from the covariant ones are developed. The first one proceeds by restriction to an invariant subspace and is exemplified in the case of massive integer spin representations of the Poincaré group. The second method takes quotients and is particularly useful when we deal with reducible but indecomposable representations. A family of stepped gauge transformations is generated when the method is used to obtain the covariant massless integer helicity representations of the Poincaré group; the electromagnetic and gravitational gauge transformations are just the first two cases of such a family.