Fischer, A. E. and J. E. Marsden
Our purpose here is to present the current state of affairs from our own point of view. We shall use geometric methods developed by the authors to establish various connections between the above-mentioned topics. The main tools we shall use to develop this material are nonlinear functional analysis, an adjoint formalism for Hamiltonian field theories, and infinite-dimwensional symplectic geometry. As we shall see, these tools and the topics we shall consider are naturally related.