Heiss, Stephan and Weigert, S. (2001) Discrete Moyal-type representations for a spin. Physical Review A. art no. 012105. ISSN 1050-2947
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.
|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:||26 Apr 2015 06:02|