Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

Details Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

2001-10-12

arxiv.org/abs/hep-th/0110114v3

Int.J.Mod.Phys.A17:297-316,2002

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 22 pages, 2 figures

Scientific paper

10.1142/S0217751X02006079

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 (eg, 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.

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