DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE

By C. K. Zachos. International Journal of Modern Physics A, 2001

172 citations recorded by the source corpus.

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by 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 — coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba00b6734a60d58320f5160edc2c7967f1b2afc1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Black hole attractors and the topological string (2004, background): “This is familiar in the reformulation of quantum mechanics as a deformation quantization (see [44] for a review and further references).”