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The overlap concept of Clebsch-Gordan coefficients and Racah lemma constants

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  • Schäffer, Claus E.

Abstract

By virtue of the isomorphic relationship between simple tensor products |l1t1〉|l2t2〉, formed from othonormal bases of real functions, and the corresponding operators Ŝl1t1l2t2 = |l1t1〉〈l2t2| obtains analogous overlap expressions (scalar products) for functions and operators when using the trace definition of operator overlap. Defining R3-irreducible tensorial quantities [|l1{⊗}l2|]l3t3 (for functions) and [|l1{ ⊗ }l2|]l3t3 (for operators) by the same expansion formulae, one makes Clebsch-Gordan coefficients expressible as function overlaps of the type 〈l1t1|〉l2t2|[|l1{ ⊗ |l2{]l3t3 and as operator overlaps of the type 〈Ŝl1t1l2t2|[|l1{ ⊗ }l2|]l3t3〉. Similarly, Racah lemma constants (isoscalar factors) obtain overlap interpretations.

Suggested Citation

  • Schäffer, Claus E., 1982. "The overlap concept of Clebsch-Gordan coefficients and Racah lemma constants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 28-49.
  • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:28-49
    DOI: 10.1016/0378-4371(82)90257-6
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    Cited by:

    1. Yudson, V.I., 1990. "Covariant approach to the wilson renormalization of nonlinear σ models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(1), pages 140-148.

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