
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 finitedimensional representations of the proper homogeneous Lorentz group. It is shown that the corresponding generalized ClebschGordan coefficient is expressed in the general case by the sum of the products of two factors, one of which is the generalized ClebschGordan coefficient for representations of a group of threedimensional rotations, while the other is the jsymbol whose number of parameters is 3(2r1), where r is the number of factors in the corresponding direct product. It is shown by direct calculations that with some simplification this jsymbol 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 ClebschGordan coefficient (the case of the product of two representations) for Lorentz group representations, which they also use to express generalized ClebschGordan coefficients. (Author)
Descriptors : (*GROUPS(MATHEMATICS), MATRICES(MATHEMATICS)), (*MATRICES(MATHEMATICS), GROUPS(MATHEMATICS)), THEORY, USSR
Distribution Statement : APPROVED FOR PUBLIC RELEASE