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

Journal Article · Sat Jan 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3533393· OSTI ID:21501243

Conrady, Florian ^[1]; Hnybida, Jeff ^[1]

---

1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada)

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.

• OSTI ID: 21501243
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 1; Other Information: DOI: 10.1063/1.3533393; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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