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Classical field theory on Lie algebroids: variational aspects. (English) Zbl 1073.70024

Summary: The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function, we study the problem of finding critical points of the action functional when we restrict the fields to being morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincaré and Lagrange-Poincaré cases), sigma models or Chern-Simons theories.

MSC:

70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70G75 Variational methods for problems in mechanics
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
49S05 Variational principles of physics
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