Computing Generalized Racah and Clebsch-Gordan Coefficients for U(N) groups
نویسنده
چکیده
After careful introduction and discussion of the concepts involved, procedures are developed to compute Racah and Clebsch-Gordan coefficients for general r-fold tensor products of the U(N) groups. In the process, the multiplicity of a given irreducible representation (irrep) in the direct sum basis is computed, and generalized Casimir operators are introduced to uniquely label the multiple irreps. Procedures to compute the Gel’fand-Zetlin basis are also included, as the Clebsch-Gordan coefficients are computed in this basis. Examples from SU(2), SU(3), and SU(4) are provided.
منابع مشابه
25 v 1 1 5 O ct 1 99 9 Multiplicity , Invariants and Tensor Product Decompositions of Tame Representations of U ( ∞ )
The structure of r-fold tensor products of irreducible tame representations of U(∞) = lim −→U(n) are described, versions of contragredient representations and invariants are realized, and methods of calculating multiplicities, Clebsch-Gordan and Racah coefficients are given using invariant theory on Bargmann-Segal-Fock spaces. PACS codes: 02.20.Tw, 02.20.QS, 03.65.Fd
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