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Discrete Moyal-type representations for a spin

Heiss, Stephan and Weigert, S. (2001) Discrete Moyal-type representations for a spin. Physical Review A. art no. 012105. ISSN 1050-2947

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Abstract

In Moyal’s formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e., by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P or Q symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels that give rise to discrete symbols. Now operators are represented by functions taking values on (2s+1)2 points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism.

Item Type: Article
Copyright, Publisher and Additional Information: © 2001 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 16 Oct 2014 19:52
Published Version: http://dx.doi.org/10.1103/PhysRevA.63.012105
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1370

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