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

TLDR: In this article, 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 Sp(4,R) and Sp(6,R).

Abstract: In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 〈λd+n/2,...,λ1+n/2〉 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 unitary‐operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of λ1,...,λd, subject to the conditions λ1≥λ2≥ ⋅ ⋅ ⋅ ≥λd≥0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisf...