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

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

1998-03-25

arxiv.org/abs/quant-ph/9803067v1

Annals Phys. 266 (1998) 503-523

Physics

Quantum Physics

20 pages,no figures,to appear in Ann. Phys.(N.Y)

Scientific paper

10.1006/aphy.1998.5805

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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