Generalized Weyl-Wigner map and Vey quantum mechanics

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalizati on of Moyal theory, also known as Vey quantum mechanics, was presented in t he literature many years ago. However, a derivation of the formalism direct ly from standard operator quantum mechanics, clarifying the relation betwee n the two formulations, is still missing. In this article we present a cova riant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpr etation of the Vey theory including a direct implementation of unitary oper ator transformations as phase space coordinate transformations in the Vey i diom. These features are illustrated through a simple example. (C) 2001 Ame rican Institute of Physics.