XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018 VII School on Geometry and Physics 25-29.06.2018
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# 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

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