Quantum Mechanics in Phase Space An Overview with Selected Papers

It has been useful in describing transport in quantum optics; nuclear physics; and quantum computing, decoherence, and chaos. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter century: It furnishes a third, alternative formulation of quantum mechanics, independent of the conventional Hilbert space or path integral formulations.
In this logically complete and self-standing formulation, one need not choose sides between coordinate and momentum space. It works in full phase-space while accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. The variables (observables) in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, but which compose together in novel algebraic ways.
This volume is a selection of 23 classic and/or useful papers about the phase-space formulation, with an introductory overview that provides a trail-map to these papers, and with an extensive bibliography. The overview collects often-used formulas and simple illustrations, suitable for applications to a broad range of physics problems, as well as teaching. It thereby provides supplementary material that may be used for a beginning graduate course in quantum mechanics.


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