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Wigner-Weyl correspondence in quantum mechanics for continuous and discrete systems-a Dirac-inspired view

Chaturvedi, S and Ercolessi, E and Marmo, G and Morandi, G and Mukunda, N and Simon, R (2006) Wigner-Weyl correspondence in quantum mechanics for continuous and discrete systems-a Dirac-inspired view. In: Journal Of Physics A-Mathematical And General, 39 (6). pp. 1405-1423.

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Official URL: http://www.iop.org/EJ/article/0305-4470/39/6/014/a...

Abstract

Drawing inspiration from Dirac's work on functions of non-commuting observables, we develop an approach to phase-space descriptions of operators and the Wigner-Weyl correspondence in quantum mechanics, complementary to standard formulations. This involves a two-step process: introducing phase-space descriptions based on placing position dependences to the left of momentum dependences (or the other way around); then carrying out a natural transformation to eliminate a kernel which appears in the expression for the trace of the product of two operators. The method works uniformly for both continuous Cartesian degrees of freedom and for systems with finite-dimensional state spaces. It is interesting that the kernel encountered is naturally expressible in terms of geometric phases, and its removal involves extracting its square root in a suitable manner.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Iop Publishing Ltd.
Keywords:
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 15 Apr 2009 04:54
Last Modified: 19 Sep 2010 04:58
URI: http://eprints.iisc.ernet.in/id/eprint/17880

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