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

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.

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

References in corpus (2)

• W(infty)-Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
• Quantum Deformed Canonical Transformations, W_{\infty}-algebras and Unitary Transformations

Cited by in corpus (3)

• The Moyal-Lie Theory of Phase Space Quantum Mechanics
• Autonomous generation of all Wigner functions and marginal probability densities of Landau levels
• $\hslash$-independent Universality of the Quantum-Classical Canonical Transformations