Realization in phase space of general coordinate transformations

We realize a subgroup of the full general field-dependent coordinate transformation group for a field theory in a certain phase space. For a pseudo-Riemannian metric in four dimensions, subject to certain conditions, this program leads uniquely to Einstein's theory of gravitation in Hamiltonian form. The framework is also applied to the Nambu-Goto string model, where again reparametrization covariance determines the dynamics.