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Title: Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

Abstract

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states are defined explicitly and related to SU(1,1) and SU(2) matrix elements.

Authors:
 [1];  [1]
  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada)
Publication Date:
OSTI Identifier:
21501243
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 52; Journal Issue: 1; Other Information: DOI: 10.1063/1.3533393; (c) 2011 American Institute of Physics; Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; IRREDUCIBLE REPRESENTATIONS; MATRIX ELEMENTS; SL GROUPS; SU-2 GROUPS; UNITARY SYMMETRY; LIE GROUPS; SU GROUPS; SYMMETRY; SYMMETRY GROUPS

Citation Formats

Conrady, Florian, Hnybida, Jeff, and Department of Physics, University of Waterloo, Waterloo, Ontario. Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases. United States: N. p., 2011. Web. doi:10.1063/1.3533393.
Conrady, Florian, Hnybida, Jeff, & Department of Physics, University of Waterloo, Waterloo, Ontario. Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases. United States. https://doi.org/10.1063/1.3533393
Conrady, Florian, Hnybida, Jeff, and Department of Physics, University of Waterloo, Waterloo, Ontario. 2011. "Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases". United States. https://doi.org/10.1063/1.3533393.
@article{osti_21501243,
title = {Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases},
author = {Conrady, Florian and Hnybida, Jeff and Department of Physics, University of Waterloo, Waterloo, Ontario},
abstractNote = {We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states are defined explicitly and related to SU(1,1) and SU(2) matrix elements.},
doi = {10.1063/1.3533393},
url = {https://www.osti.gov/biblio/21501243}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 1,
volume = 52,
place = {United States},
year = {Sat Jan 15 00:00:00 EST 2011},
month = {Sat Jan 15 00:00:00 EST 2011}
}