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

Miloslav Havlíček; Jan Kotrbatý; Patrick Moylan; Severin Pošta

doi:10.1088/1742-6596/1194/1/012043

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

Miloslav Havlíček
, Jan Kotrbatý
, Patrick Moylan
, Severin Pošta

Division of Engineering and Science (Abington)

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

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 W_r(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 language	English (US)
Article number	012043
Journal	Journal of Physics: Conference Series
Volume	1194
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/1194/1/012043
State	Published - Apr 24 2019
Event	32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic Duration: Jul 9 2018 → Jul 13 2018

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1088/1742-6596/1194/1/012043

Cite this

@article{aa52aa13b570402881973b6bf056658e,

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.",

author = "Miloslav Havl{\'i}{\v c}ek and Jan Kotrbat{\'y} and Patrick Moylan and Severin Po{\v s}ta",

note = "Publisher Copyright: {\textcopyright} 2019 Published under licence by IOP Publishing Ltd.; 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2019",

month = apr,

day = "24",

doi = "10.1088/1742-6596/1194/1/012043",

language = "English (US)",

volume = "1194",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

TY - JOUR

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

AU - Havlíček, Miloslav

AU - Kotrbatý, Jan

AU - Moylan, Patrick

AU - Pošta, Severin

PY - 2019/4/24

Y1 - 2019/4/24

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85065573256

UR - https://www.scopus.com/pages/publications/85065573256#tab=citedBy

U2 - 10.1088/1742-6596/1194/1/012043

DO - 10.1088/1742-6596/1194/1/012043

M3 - Conference article

AN - SCOPUS:85065573256

SN - 1742-6588

VL - 1194

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012043

T2 - 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018

Y2 - 9 July 2018 through 13 July 2018

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this