From the discrete Weyl -- Wigner formalism for symmetric ordering to a number -- phase Wigner function

Abstract

The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on the discrete phase space is found and the limit, when the dimension of Hilbert space tends to infinity, is considered. It is shown that this limit gives the number -- phase Wigner function in quantum optics. Analogous results for the `almost' symmetric ordering in an even -- dimensional Hilbert space are obtained. Relations between the discrete Wigner functions introduced in our paper and some other discrete Wigner functions appearing in literature are studied.

28 pages

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Cited by in corpus (3)

• The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin
• Orbital-Free Quasi-Density Functional Theory
• The Weyl -- Wigner -- Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function