Accession Number : AD0622736

Title :   THE GENERALIZATION OF THE WIGNER-RACAH ANGULAR MOMENTUM CALCULUS, II,

Corporate Author : EUROPEAN COUNCIL FOR NUCLEAR RESEARCH GENEVA (SWITZERLAND)

Personal Author(s) : Biedenharn,L. C.

Report Date : 08 JAN 1965

Pagination or Media Count : 2

Abstract : The very great importance in all branches of quantum physics of the Wigner-Racah angular momentum calculus has led to many attempts to generalize this structure from the two-dimensional unimodular unitary ('angular momentum') group, where it originated, to the general semi-simple compact Lie group. A solution to the various problems connected with this generalization, in particular the problem of simple reducibility, has been sketched in an earlier note (AD-613 412), and the detailed proofs of the results stated there have been obtained. The purpose of the present note is to show that this generalization is a canonical resolution of the multiplicity problem, explicitly for all SU sub n and thereby implicity for all other groups in question by imbedding in SU sub n. The method is especially interesting in that it demonstrates a new significance for the Racah coefficients, and shows the existence of intriguing continuum limit properties for the generalized Racah and Wigner coefficients. Proofs of the assertions to be made below will be given elsewhere, but the structure of the results to be presented is rather elegant and should be easily accessible.

Descriptors :   (*MOMENTUM, OPERATORS(MATHEMATICS)), (*OPERATORS(MATHEMATICS), MOMENTUM), PERTURBATION THEORY, GROUPS(MATHEMATICS), QUANTUM THEORY, CALCULUS OF VARIATIONS, ALGEBRA

Distribution Statement : APPROVED FOR PUBLIC RELEASE