  We deform the moment map picture on the space of symplectic connections on a
symplectic manifold. To do that, we study a vector bundle of Fedosov star
product algebras on the space of symplectic connections. We describe a natural
formal connection on this bundle adapted to the star product algebras on the
fibers. We study its curvature and show the star product trace of the curvature
is a formal symplectic form on the space of symplectic connections. The action
of Hamiltonian diffeomorphisms on symplectic connections preserves the formal
symplectic structure and we show the star product trace can be interpreted as a
formal moment map for this action. Finally, we apply this picture to study
automorphisms of star products and Hamiltonian diffeomorphisms.
