Euler-Poincare equations for field theories

Marco Castrillon, University of Madrid

In this talk I am going to present the analogue of the Euler-Poincare reduction for Lagrangian Field Theories. The geometry of the the so called bundle of connections will play an important role and I will review some of its properties. I will also present the reconstruction process and I will show that some compatibility conditions (with a clear geometrical interpretation) are needed. This compatibility conditions do not appear in the reconstruction process in Mechanics. Some examples of the theory will be provided an the end of the talk.