Abstract:If a Lagrangian field theory admits local symmetries, its initial value problem is not well-posed. Making the initial value problem well-posed generally involves two steps: imposing constraints and gauge fixing. It is well known that in the case of gauge theories this two step procedure can be understood as symplectic reduction. I will explain how to generalize this approach to field theories with external symmetries such as general relativity, where the symmetry group acts also on the base of the configuration bundle. This is joint work with Alan Weinstein.