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Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases (1007.0937v2)
Published 6 Jul 2010 in gr-qc
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 J3 and a continuous basis diagonalized by K1, 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.