M. Przanowski et J. Tosiek, The Weyl-Wigner-Moyal formalism. III. The generalized Moyal product in thecurved phase space, ACT PHY P B, 30(2), 1999, pp. 179-201
Construction of the symplectic connection on phase space is proposed. This
connection is in a sense defined by the Riemannian connection on the config
uration space. The generalized Moyal product leading to the quantum multipl
ication in the curved phase space is given.