Construction of representations of Poincaré group using Lie fields

Miloslav Havlíček; Jan Kotrbatý; Patrick Moylan; Severin Pošta

doi:10.1063/1.4993153

Construction of representations of Poincaré group using Lie fields

Miloslav Havlíček, Jan Kotrbatý, Patrick Moylan, Severin Pošta

Division of Engineering and Science (Abington)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English (US)
Article number	021702
Journal	Journal of Mathematical Physics
Volume	59
Issue number	2
DOIs	https://doi.org/10.1063/1.4993153
State	Published - Feb 1 2018

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4993153

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title = "Construction of representations of Poincar{\'e} group using Lie fields",

abstract = "In this paper, we give an explicit construction of the unitary irreducible representations of the Poincar{\'e} groups in 2, 3, and 4 space-time dimensions on Hilbert spaces associated with the Schr{\"o}dinger 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 Poincar{\'e} algebras.",

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AU - Moylan, Patrick

AU - Pošta, Severin

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N2 - 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.

AB - 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.

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Construction of representations of Poincaré group using Lie fields

Abstract

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