Nontrivial extensions of a representation of the Poincaré group with mass and helicity zero by its tensorial product (Q1080964)

Let U(a,\(\Lambda)\) be a representation of the Poincaré group with mass and helicity zero. The nontriviality of the cohomology of extension of such a representation by its tensorial product is established. More precisely each equivalence class is indexed by a pair (u(\(\lambda)\),\(\alpha)\) where \(\alpha\in {\mathbb{C}}\) and u(\(\lambda)\) is a distribution in \({\mathcal D}'_{]0,1[}\). This result is of interest for quantum theories with an indefinite metric. Conversely, in the nonzero mass case, the same cohomology is trivial [\textit{E. Taflin}, Preprint, Univ. Genève, UGVA.DPT 1983/02-376)].