Coherent state triplets and their inner products

Details Coherent state triplets and their inner products Coherent state triplets and their inner products

2002-05-22

arxiv.org/abs/math-ph/0205034v2

Physics

Mathematical Physics

33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being corrected

Scientific paper

10.1063/1.1509851

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.

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