Classical field theory on Lie algebroids: Variational aspects

Abstract

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 be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.

Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References added

References in corpus (1)

• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries

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• Discrete Lagrangian field theories on Lie groupoids
• Differential geometry, Palatini gravity and reduction
• Poisson structures on almost complex Lie algebroids
• K-symplectic formalism on Lie algebroids
• Killing sections and sigma models with Lie algebroid targets
• Reduced classical field theories. k-cosymplectic formalism on Lie algebroids
• Linearization of nonlinear connections on vector and affine bundles, and some applications
• Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor