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 second-order 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 non-trivial 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 Laplace-Beltrami 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