HAVLÍČEK, M., et al. Construction of representations of Poincaré group using Lie fields. Journal of Mathematical Physics. 2018, 59(2), ISSN 0022-2488. DOI 10.1063/1.4993153.
In this paper, we give an explicit construction of the unitary irreducible representations of the Poincaré groups in 2, 3, and 4 space-time dimensions on Hilbert spaces associated with the Schrödinger representation of the Weyl algebra for n = 1, 2, and 3, respectively. Our method of constructing the representations uses extension and localization of the enveloping algebras associated with these Weyl algebras and the Poincaré algebras.