W infinity-covariance of the Weyl-Wigner-Groenewold-Moyal quantization

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Dereli T., Vercin A.

JOURNAL OF MATHEMATICAL PHYSICS, vol.38, no.11, pp.5515-5530, 1997 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 11
  • Publication Date: 1997
  • Doi Number: 10.1063/1.532149
  • Page Numbers: pp.5515-5530


The differential structure of operator bases used in various forms of the Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a derivative-based approach, alternative to the conventional integral-based one is developed. Thus the fundamental quantum relations follow in a simpler and unified manner. An explicit formula for the ordered products of the Heisenberg-Weyl algebra is obtained. The W-infinity-covariance of the WWGM-quantization in its most general form is established. It is shown that the group action of W-infinity that is realized in the classical phase space induces on bases operators in the corresponding Hilbert space a similarity transformation generated by the corresponding quantum W-infinity which provides a projective representation of the former W-infinity. Explicit expressions for the algebra generators in the classical phase space and in the Hilbert space are given. It is made manifest that this W-infinity-covariance of the WWGM-quantization is a genuine property of the operator bases. (C) 1997 American Institute of Physics.