Symplectic quantum mechanics
The present paper addresses the problem of constructing unitary representations of the Galilei group and reinterpreting the Schrödinger equation in phase space, via symplectic geometry and the Weyl *-product. In this way, an alternative route to Wigner functions is established, not relying on the Liouville- von Neumann equation. Subsequently, applications to linear and nonlinear oscillators are presented, and the notion of coherent state discussed. The article is clearly written, and its methods and results may be usefully compared with other approaches in the same vein (see e.g., [\textit{S. T. Ali}, \textit{J.-P. Antoine}, \textit{J.-P. Gazeau} and \textit{U. A. Mueller}, Coherent states and their generalizations: A mathematical overview Rev. Math. Phys. 7 No. 7, 1013--1104 (1995; Zbl 0837.43014)], [\textit{S. T. Ali}, [Quantization techniques: a quick overview, in: Contemporary problems in mathematical physics (Cotonu 2001) 3--78 (River Edge, NJ, World Scientific) (2002; Zbl 1044.81068)] and references therein).
scientific article; zbMATH DE number 2092928