Equivalence of a class of Wigner coefficients of SU(1,1) with those of SU(2)
Por:
Chacón E., Levi D., Moshinsky M.
Publicada:
1 ene 1974
Resumen:
The purpose of this note is to establish the relation (? 1?2?1?2|?M) nc = (- 1)?2 - ?2?(1/2)(M + ?1 -?2 -1), (1/2)(M + ?2 - ?1 - 1), (1/2)(?1 - ?2 + ?1 + ?2 - 1), (1/2)(?2 - ?1 + ?1 + ?2 - 1)|? - 1,?1 + ?2 - 1?, where the left-hand side is a Wigner coefficient of the noncompact group SU(1,1) and in the right-hand side appears a standard Wigner coefficient of SU(2). The parameters ?1, ?2, ? characterize unitary irreducible representations in the positive discrete series of SU(1,1), and thus they take positive integer or half-integer values. The other parameters are restricted by ?1 = ?1,?1 + 1,?1 + 2,?, ?2 = ?2,?2 + 1,?2 + 2,?, M = ?,? + 1,? + 2,?. Besides we have ?1 + ?2 = M and ? = ?1 + ?2,?1 + ?2 + 1,?. A similar result is obtained [cf. our Eq. (3.28)] for Wigner coefficients involving unitary irreducible representations of the negative discrete series of SU(1,1). Copyright © 1975 American Institute of Physics.
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