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

Claus E. Schäffer

Physica A: Statistical Mechanics and its Applications, 1982, vol. 114, issue 1, 28-49

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.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:114:y:1982:i:1:p:28-49

DOI: 10.1016/0378-4371(82)90257-6

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