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Coherent state triplets and their inner products
- 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33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being corrected
- Subjects :
- Sequence
Pure mathematics
Group (mathematics)
Hilbert space
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Group Theory (math.GR)
Space (mathematics)
Measure (mathematics)
symbols.namesake
Product (mathematics)
Linear algebra
symbols
FOS: Mathematics
Coherent states
Mathematics - Group Theory
Mathematical Physics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....37dd83d1b6e8ada82450e9bd9d1a9619
- Full Text :
- https://doi.org/10.48550/arxiv.math-ph/0205034