Clebsch-Gordan Formulas of the SU(1, 1) Group
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概要
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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 formula 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 Clebsch-Gordan 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 polynomials- belong 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.
- 理論物理学刊行会の論文
- 1970-09-25
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