2001/10/31 by Cosmas K Zachos · 1 citation
Physics and Astronomy · #hep-th #quant-ph
paper · pdf · doi:10.1142/s0217751x02006079
published as Int.J.Mod.Phys.A17:297-316,2002 · LaTeX, 22 pages, 2 figures
arxiv created 2002/01/09 · arxiv updated 2009/11/30
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.