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Metaplectic Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization and Beyond

A. Vercin
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Abstract

The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of this quantization scheme is investigated, and explicit expressions for the quantum-deformed Hamiltonian vector fields are presented. In a general basis the structure constants of the $W_{\infty}$-algebra are obtained and its subalgebras are analyzed.

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A. Vercin. 1998-03-25. Metaplectic Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization and Beyond. https://doi.org/10.1006/aphy.1998.5805

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