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Fortschritte der Physik/Progress of Physics

On the Moyal Formulation of Quantum Identical Particles

Manuel Gadella, Luis Miguel Nieto

Published Jan 1, 1994• 4 citations
Publisher

Abstract

Wigner functions of permutation operators are obtained and are used as a basis for a phase space formulation of quantum identical particles. Non-spin systems as well as 1/2 spin systems are considered. The general results are applied to a couple of examples.
DOI
10.1002/prop.2190420303

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Some Applications of the Coherent State Formulation of the Wigner Operator

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On the basis of the preceding paper we present some new applications of both the normal product form and the coherent state form of the Wigner operator, which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.

Communications in Theoretical Physics•May 1, 1984•44 citations
Abstract The Weyl‐Wigner‐Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space and functions on the phase space is found. The expressions for the Stratonovich‐Weyl quantiser, star product and Wigner functions of such systems for arbitrary values of spin are obtained in detail. As examples the Landau levels and the corresponding Wigner functions for a spin nonrelativistic particle as well as the magnetic resonance for a spin nonrelativistic uncharged particle are analysed.
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This chapter presents Wigner’s approach to quantum mechanics, based on the Wigner function in phase space. It explains Wigner–Weyl quantization, which makes it possible to associate functions on phase space to wave functions and operators, and it develops the technology to do quantum mechanics in this formalism. This includes the star product, Moyal evolution, and star-eigenvalue equations. It also develops semiclassical methods in this formulation, and it has a section on Berry’s semiclassical formula for the Wigner function in one-dimensional systems.
On the basis of the preceding paper we present some new applications of both the normal product form and the coherent state form of the Wigner operator, which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.