An algebraic algorithm for calculating Clebsch{endash}Gordan coefficients; application to SU(2) and SU(3)
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7 (Canada)
- Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3 (Canada)
A recent paper gave an explicit construction for inducing shift tensors of a compact reductive Lie group from shift tensors of a suitably defined subgroup. The shift tensors were defined on model spaces of holomorphic vector-coherent-state wave functions. In this paper, we use these shift tensors to obtain an algorithm for computing Clebsch{endash}Gordan coefficients. The approach reproduces the known analytical results for SU(2) and gives a simple algorithm for computing SU(3) coefficients. The algorithm is shown to yield analytical expressions for the multiplicity-free SU(3) couplings of type ({lambda}{sub 2}0){circle_times}({lambda}{sub 1}0).{copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 526902
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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