Casimir operators, duality, and the point groups

Autor:	J. J. Sullivan, T. H. Siddall
Rok vydání:	1992
Předmět:	Casimir effect Symmetric group Group (mathematics) Quantum mechanics Duality (optimization) Statistical and Nonlinear Physics Angular momentum operator Casimir element Point group Mathematical Physics Mathematical physics Mathematics Spin-½
Zdroj:	Journal of Mathematical Physics. 33:1964-1969
ISSN:	1089-7658 0022-2488
DOI:	10.1063/1.529671
Popis:	In atomic or nuclear shell theory the quadratic Casimir operators can be used to evaluate the expectation values of two‐body interactions among equivalent members of a shell. Racah has given closed expressions for these Casimir operators for all the groups in the Racah chain. In this paper an alternate derivation of these closed expressions based on duality with the symmetric group is given. The derivation allows extension of these expressions to situations in which equivalent spins are in an environment, such as a point group, for which the two‐body interactions separate into distinct sets. Possible application to NMR systems with spin ≥1/2 are discussed.
Databáze:	OpenAIRE
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