Massless particles, conformal group, and de Sitter universe

Abstract

We first review a recent result on the uniqueness of the extension to the conformal group of massless representations of the Poincar\'e group. By restricting these representations to SO(3,2) we obtain a unique definition of massless particles in de Sitter space. This definition is compared with the concept of masslessness that arises from considerations of gauge invariance. Next, we recall the startling fact that the direct product of two Dirac singleton representations of SO(3,2) decomposes into a direct sum of the massless representations of SO(3,2). A theory of interacting singleton fields is developed and a simple expression is given for the intertwining operator between massless fields and two-singleton fields. Finally, we discuss the behavior of these massless representations with respect to the contraction of the deSitter group to the Poincar\'e group.