(Heisenberg-)Weyl Algebras, Segal-Bargmann Transform and Representations of Poincaré Groups

Miloslav Havlíček, Jan Kotrbatý, Patrick J. Moylan, Severin Pošta

Research output: Contribution to journalConference article

Abstract

In a recent paper [1] we described a novel treatment of the unitary irreducible representations of the Poincaré groups in 2, 3 and 4 space-time dimensions as unitary operators on the representation spaces of the Schrodinger representation of the Heisenberg-Weyl algebra Wr(ℝ) of index r = 1, 2, and 3, respectively. Here we relate this approach to the usual method of describing the representations of these Poincare groups, i.e. the Wigner-Mackey construction.

Original languageEnglish (US)
Article number012043
JournalJournal of Physics: Conference Series
Volume1194
Issue number1
DOIs
StatePublished - Apr 24 2019
Event32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic
Duration: Jul 9 2018Jul 13 2018

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algebra
operators

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "(Heisenberg-)Weyl Algebras, Segal-Bargmann Transform and Representations of Poincar{\'e} Groups",
abstract = "In a recent paper [1] we described a novel treatment of the 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 Schrodinger representation of the Heisenberg-Weyl algebra Wr(ℝ) of index r = 1, 2, and 3, respectively. Here we relate this approach to the usual method of describing the representations of these Poincare groups, i.e. the Wigner-Mackey construction.",
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(Heisenberg-)Weyl Algebras, Segal-Bargmann Transform and Representations of Poincaré Groups. / Havlíček, Miloslav; Kotrbatý, Jan; Moylan, Patrick J.; Pošta, Severin.

In: Journal of Physics: Conference Series, Vol. 1194, No. 1, 012043, 24.04.2019.

Research output: Contribution to journalConference article

TY - JOUR

T1 - (Heisenberg-)Weyl Algebras, Segal-Bargmann Transform and Representations of Poincaré Groups

AU - Havlíček, Miloslav

AU - Kotrbatý, Jan

AU - Moylan, Patrick J.

AU - Pošta, Severin

PY - 2019/4/24

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AB - In a recent paper [1] we described a novel treatment of the unitary irreducible representations of the Poincaré groups in 2, 3 and 4 space-time dimensions as unitary operators on the representation spaces of the Schrodinger representation of the Heisenberg-Weyl algebra Wr(ℝ) of index r = 1, 2, and 3, respectively. Here we relate this approach to the usual method of describing the representations of these Poincare groups, i.e. the Wigner-Mackey construction.

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