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

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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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Citation Formats

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.