Hamiltonian analysis of the Schroedinger field coupled with dynamic non-relativistic gravity

Using the recently mooted Galilean gauge theory we have constructed the model for the Schroedinger field interacting wuth gravity which is also dynamical. The dynamics of gravity is dictated by the Newtonian action in the Newton-Cartan spacetime. The theory is highly constrained . An elaborate analysis of the constraints of the theory have been performed. The symmetries are explicitly verified and the uniqueness of the model has been established. To the best of our knowledge both the model and its constraints structure are unique in the literature