Patrick Moylan

Heisenberg-Weyl Algebras and Representations of Poincar\'e Groups

We give a novel description of unitary irreducible representations of the Poincar\'e groups in 2, 3 and 4 space-time dimensions as unitary operators on the representation spaces of the Schr\"odinger representation of the Heisenberg-Weyl algebra ${\bf W}_n(\mathbb{R})$ of index $n$ = 1, 2, and 3, respectively. We relate this approach to the usual method of describing the representations of Poincar\'e groups, i.e. the Wigner-Mackey construction.

Event sponsored by:
University of Bialystok