
Accession Number : AD0664307
Title : A GENERAL STUDY OF THE WIGNER COEFFICIENTS OF SU(1,1),
Corporate Author : MIAMI UNIV CORAL GABLES FLA CENTER FOR THEORETICAL STUDIES
Personal Author(s) : Holman,Wayne J. , III ; Biedenharn,Lawrence C. , Jr
Report Date : 1968
Pagination or Media Count : 34
Abstract : The Wigner coefficients which couple any two irreducible unitary representations of the noncompact group SU(1,1) are derived by means of the secondorder difference equation which defines them. It is found that whenever at least one of the three representations being coupled is discrete, then the two solutions are degenerate, but two linearly independent nontrivial solutions exist, in general, when all three representations are continuous. For this case two orthonormal solutions are found. Some elementary symmetries of the solutions are examined. The integral over the group manifold is regularized by means of a convergence factor in order to make all the irreducible unitary representation functions (the Bargmann functions) mutually orthonormal. This regularization is used for the investigation of the resolvent of the LaplaceBeltrami operator in the space of the Bargmann functions. (Author)
Descriptors : (*ELEMENTARY PARTICLES, *GROUPS(MATHEMATICS)), MOMENTUM, INTERACTIONS, OPERATORS(MATHEMATICS), QUANTUM THEORY, INTEGRALS, SPECIAL FUNCTIONS(MATHEMATICAL), DIFFERENCE EQUATIONS
Subject Categories : Nuclear Physics & Elementary Particle Physics
Quantum Theory and Relativity
Distribution Statement : APPROVED FOR PUBLIC RELEASE