- Banach Center Publications Journal
- December 2016
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- También publicado en arXiv:1511.03302 Abstract: Inspired by problems arising in the geometrical treatment of Yang&-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1Ʈ$ on a manifold with boundary is presented. After a precise statement of Hamilton's variational principle in this context, the geometrical properties of the space of solutions of the Euler&-Lagrange equations of the theory are analyzed. A sufficient condition is obtained that guarantees that the set of solutions of the Euler&-Lagrange equations at the boundary of the manifold fill a Lagrangian submanifold of the space of fields at the boundary. Finally a theory of constraints is introduced that mimics the constraints arising in Palatini's gravity.