Invariant bilinear forms on 3 + 2 de Sitter space

Massive elementary systems in 3 + 2 de Sitter space are associated with unitary irreducible representations of the kinematic group SOo(3, 2). On the other hand, massless elementary systems are connected to certain non-decomposable representations of this group. As usual they display gauge invariance and conformal invariance properties. We give in this work the corresponding invariant bilinear forms. They are indefinite in the second case, positive-definiteness being restored on (physical) quotient spaces. In particular we present a table of scalar products involving lowest-energy states cyclic for the two Gupta-Bleuler triplets of de Sitter QED, and we examine some of its conformal invariance aspects. (author)