Nontrivial extensions of a representation of the Poincar� group with mass and helicity zero by its tensorial product

Abstract

Let U(a, Λ) be a representation of the Poincare group ℘ with mass and helicity zero, realized in the space of C∞-functions with compact support on ℝ3, without the origin. Let U(2)(a, Λ) denote the tensorial product of U(a, Λ) by itself. We explicitly determine the cocycles of extension of U(a, Λ) by U(2)(a, Λ) and we prove that the nontrivial cohomology is indexed by (u(λ),α),u(λ)∈D1]0,3\,α∈ℂ.