Automorphisms of the Weyl manifold

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 $\check{\mathrm{C}}$ech cocycle corresponding to the symplectic structure $\omega$.) $[c_0+{\sum }_{\mathrm{\ell }=1}^{\mathrm{\infty }}{c}_{\mathrm{\ell }}{\nu }^{2\mathrm{\ell }}]\in {\check{H}}^2(M)[[{\nu }^2]]$. We also construct modified contact Weyl diffeomorphisms.