The Hamilton-Pontryagin principle for Classical Field theories

Dr. Joris Vankerschaver, Control & Dynamical Systems, Caltech

In this talk I will discuss an extension of the Hamilton-Pontryagin principle for field theories on a fiber bundle.  The bulk of the talk will be a gentle introduction to the dynamics of field theories, and I will indicate how the Hamilton-Pontryagin principle can be extended in a natural way to this setting.  Moreover I will point out how similar variational principles have occurred in the literature on continuum dynamics, and what their respective advantages are.  Time permitting, I will also discuss the case of "reparametrized field theories", where the space-time variables are included among the fields and the link with the 3+1 formulation of general relativity. This setup may be relevant for the design of mesh-adapting numerical integrators.