相干态三重态及其内积
Coherent state triplets and their inner products
摘要：
证明了：若H是群G的一个表示的Hilbert空间，则存在空间F_H，H，F^H的三元组，其中F^H是相干态或矢量相干态波函数的空间，F_H是它相对于一个方便定义的测度的对偶.还证明了存在一个映射序列F_H -> H -> F^H，它便于构造相应的内积.在必要时完成之后，F_H，H和F^H，成为同构的希尔伯特空间。结果表明，H的内积在F_H中往往比在F^H中更容易计算.从而得到了相干态和矢量相干态表象的内积的积分表达式。这些表达式等价于K-矩阵理论的代数表达式，但它们通常更有效地应用。该构造通过许多实例来说明。
英文摘要：
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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