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Search: MSC category 81S30 ( Phase-space methods including Wigner distributions, etc. )

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1. CJM 1999 (vol 51 pp. 816)

Hall, Brian C.
A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type
I consider a two-parameter family $B_{s,t}$ of unitary transforms mapping an $L^{2}$-space over a Lie group of compact type onto a holomorphic $L^{2}$-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B.~Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting cases $s \rightarrow \infty$ and $s \rightarrow t/2$.

Categories:22E30, 81S30, 58G11

2. CJM 1997 (vol 49 pp. 160)

Rieffel, Marc A.
The Classical Limit of Dynamics for Spaces Quantized by an Action of ${\Bbb R}^{\lowercase{d}}$
We have previously shown how to construct a deformation quantization of any locally compact space on which a vector group acts. Within this framework we show here that, for a natural class of Hamiltonians, the quantum evolutions will have the classical evolution as their classical limit.

Categories:46L60, 46l55, 81S30

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