Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
- 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
Similar Records
Unitary relation for the time-dependent SU(1,1) systems
The unitary irreducible representations of SU(2,1)