K-symplectic formalism on Lie algebroids

Details K-symplectic formalism on Lie algebroids K-symplectic formalism on Lie algebroids

2009-05-28

arxiv.org/abs/0905.4585v1

J.Phys.A42:385209,2009

Physics

Mathematical Physics

35 pages

Scientific paper

10.1088/1751-8113/42/38/385209

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson sigma models.

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