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

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 formW∞-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 theW∞-algebra are obtained and its subalgebras are analyzed.