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 SO(0)(3,2). On the other hand, massless elementary systems are connected to certain nondecomposable representations of this group. As usual they display gauge invariance and conformal invariance properties. The corresponding invariant bilinear forms are given here. They are indefinite in the second case, positive-definiteness being restored on (physical) quotient spaces. A table of scalar products involving lowest-energy states cyclic is given for the two Gupta-Bleuler triplets of de Sitter QED and some of its conformal invariance aspects are made precise.