Clebsch - Gordan Formulas of the SU ( l , I ) Group
نویسنده
چکیده
The Clebsch-Gordan formulas for d-function are studied for both nonunitary finite dimensional representation and unitary infinite dimensional representation of the SU (1, 1) group. It is shown that, in addition to the usual Clebsch-Gordan formulas for the above-mentioned two representations, there exists an additional type of Clebsch-Gordan fornmla connecting the nonunitary and unitary d-functions. The new kind of Clebsch-Gordan coefficient of the SU(1, 1) obtained in our previous paper arises naturally in this formula. The three ClebschGordan formulas are proved to be interrelated with each other by analytic continuation. It is, further, pointed out that all the recurrence formulas of the unitary d-functions -obtainable from the known recurrence relations of Jacobi polynomialsbelong actually to this new type of Clebsch-Gordan formula. Explicit algebraic formulas of d-functions are derived by employing an elementary algebraic method analogous to the standard treatment of angular momentum.
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