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

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

2010-07-06

arxiv.org/abs/1007.0937v2

J. Math. Phys. 52:012501,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, no figures; v2: published version

Scientific paper

10.1063/1.3533393

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^3 and a continuous basis diagonalized by K^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.

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