Joris Vankerschaver: Abstract

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.

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