Coherent states of the real symplectic group in a complex analytic parametrization. II. Annihilation-operator coherent states

In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations , encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the annihilation-operator coherent states, i.e., the eigenstates of the noncompact lowering generators corresponding to complex eigenvalues. These states generalize the coherent states introduced by Barut and Girardello for Sp(2,R), and later on extended by Deenen and Quesne to the Sp(2d,R) irreducible representations of the type <(lambda+n/2)/sup d/>. When lambda1,...,lambda/sub d/ are not all equal, it was shown by Deenen and Quesne that the eigenvalues do not completely specify the eigenstates of the noncompact lowering generators