Accession Number : AD0616679

Title :   REDUCTION OF THE DIRECT PRODUCT OF REPRESENTATIONS OF THE PROPER HOMOGENEOUS LORENTZ GROUP,

Corporate Author : AMERICAN METEOROLOGICAL SOCIETY BOSTON MASS

Personal Author(s) : Levinson,I. B. ; Yutsis,A. P.

Report Date : AUG 1964

Pagination or Media Count : 19

Abstract : The authors examine the reduction of the direct product of any number of finite-dimensional representations of the proper homogeneous Lorentz group. It is shown that the corresponding generalized Clebsch-Gordan coefficient is expressed in the general case by the sum of the products of two factors, one of which is the generalized Clebsch-Gordan coefficient for representations of a group of three-dimensional rotations, while the other is the j-symbol whose number of parameters is 3(2r-1), where r is the number of factors in the corresponding direct product. It is shown by direct calculations that with some simplification this j-symbol is expressed by the product of 9 j symbols, the number of which is equal to r - 1. The authors give the properties of symmetry of the ordinary Clebsch-Gordan coefficient (the case of the product of two representations) for Lorentz group representations, which they also use to express generalized Clebsch-Gordan coefficients. (Author)

Descriptors :   (*GROUPS(MATHEMATICS), MATRICES(MATHEMATICS)), (*MATRICES(MATHEMATICS), GROUPS(MATHEMATICS)), THEORY, USSR

Distribution Statement : APPROVED FOR PUBLIC RELEASE