Assume that $M$ is a smooth manifold with a symplectic structure $\omega$. Then Weyl manifolds on the symplectic manifold $M$ are Weyl algebra bundles endowed with suitable transition functions. From the geometrical point of view, Weyl manifolds can be regarded as geometrizations of star products attached to $(M,\omega)$. In the present paper, we are concerned with the automorphisms of the Weyl manifold corresponding to Poincar\'e-Cartan class ($c_0$ is a $\check{ \rm C}$ech cocycle corresponding to the symplectic structure $\omega$.) $[c_0+\sum_{ \ell=1}^\infty c_{ \ell} \nu^{ 2\ell}]\in \check{ H}^2 (M)[[\nu^2]]$. We also construct modified contact Weyl diffeomorphisms.
Categories: math.DG math-ph math.MP