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W infinity-covariance of the Weyl-Wigner-Groenewold-Moyal quantization
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Date
1997-11-01
Author
Dereli, T
Vercin, A
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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.
Subject Keywords
Phase-space methods
,
Quantum-mechanics
,
Noncommuting operators
,
Deformation theory
,
Calculus
,
Coherent
,
Algebra
,
States
URI
https://hdl.handle.net/11511/65917
Journal
JOURNAL OF MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1063/1.532149
Collections
Department of Physics, Article
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T. Dereli and A. Vercin, “W infinity-covariance of the Weyl-Wigner-Groenewold-Moyal quantization,”
JOURNAL OF MATHEMATICAL PHYSICS
, pp. 5515–5530, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65917.