Chapter 9: 6j SYMBOLS AND THE RACAH COEFFICIENTS

The following sections are included:

• DEFINITION

  • 6j Symbols

  • Racah Coefficients

  • R Symbols

• GENERAL EXPRESSIONS FOR THE 6j SYMBOLS. RELATIONS BETWEEN THE 6j SYMBOLS AND OTHER FUNCTIONS

  • Expressions for the 6j Symbols in Terms of Finite Sums

  • Bargmann Formula [53]

  • Relations Between the 6j Symbols and the Generalized Hypergeometric Functions

  • Relations Between the 6j Symbols and the 3jm Symbols

  • Quasi-Binomial Representation of the 6j Symbols

• INTEGRAL REPRESENTATIONS OP THE 6j SYMBOLS

• SYMMETRIES OF THE 6j SYMBOLS AND THE RACAH COEFFICIENTS

  • R-Symbols

  • 6j Symbols

  • Racah Coefficients

  • "Mirror" Symmetry

• EXPLICIT FORMS OF THE 6j SYMBOLS FOR CERTAIN ARGUMENTS

  • One of Arguments is Equal to Zero

  • One of Arguments is Equal to the Sum of Two Others

  • One of Arguments is Smaller by Unity than the Sum of Two Others

  • Arguments a, b, d, e are Equal in Pairs

• RECURSION RELATIONS

  • Relations in Which Arguments are Changed by 1/2

  • Relations in Which Arguments are Changed by 1

• GENERATING FUNCTION

• SUMS INVOLVING THE 6j SYMBOLS

• ASYMPTOTICS OF THE 6j SYMBOLS FOR LARGE ANGULAR MOMENTA

  • Asymptotic Relations Between the 6j Symbols and the Clebsch-Gordan Coefficients

  • Asymptotic Expressions for the 6j Symbols

• RELATIONS BETWEEN THE WIGNER 6j SYMBOLS AND ANALOGOUS FUNCTIONS OF OTHER AUTHORS

• TABLES OF ALGEBRAIC EXPRESSIONS FOR THE 6j SYMBOLS

• NUMERICAL VALUES OF THE 6j SYMBOLS