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Coherent state triplets and their inner products

Authors :
Joe Repka
David J Rowe
Publication Year :
2002
Publisher :
arXiv, 2002.

Abstract

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33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being corrected

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....37dd83d1b6e8ada82450e9bd9d1a9619
Full Text :
https://doi.org/10.48550/arxiv.math-ph/0205034