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

作者：Conrady Florian^*; Hnybida Jeff

来源：Journal of Mathematical Physics, 2011, 52(1): 012501.

DOI：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.

• 出版日期2011-1