Brian C. Hall
Quantum Mechanics in Phase Space
(56K, AMS-Latex)
ABSTRACT. This paper describes a phase space representation for quantum
mechanics of a system whose configuration space is a compact Lie
group. The phase space Hilbert space is an L^2 space of holomorphic
functions, and is connected to the configuration space Hilbert
space by a generalization of the Segal-Bargmann transform.
Several aspects of the phase space representation and the transform
are discussed, including an inversion formula, a version of the
uncertainty principle, and a description of how Schrodinger operators
act in the phase space representation. This paper is expository
and will appear in Proceedings of the Summer Research Conference
on Quantization, M. Rieffel, ed., AMS Contemporary Mathematics.