Structure of the Wigner 9j Coefficients in the Bargmann Approach

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Abstract
Bargmann's treatment of the Clebsch‐Gordan (3j) and Racah (6j) coefficients is here extended to the case of Wigner 9j coefficients. The generating function for the 9j coefficient is computed by the analytic method. The result is compared to the Schwinger's expression derived with the algebraic (boson operator) method. The full symmetry of the Wigner 9j coefficients is manifest and transparent in the Bargmann's formalism. A new explicit expression for the Wigner 9j coefficient is derived as a sixfold sum which may be regarded as the analog of the Racah's formula for the Racah coefficient.

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