# Publishing house / Banach Center Publications / All volumes

## Covariant Hamiltonian first-order field theories with constraints, on manifolds with boundary: the case of Hamiltonian dynamics

### Volume 110 / 2016

Banach Center Publications 110 (2016), 87-104 MSC: 70H15, 70H25, 70S05, 53D12. DOI: 10.4064/bc110-0-6

#### 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 $1+0$ 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.

#### Authors

• A. IbortICMAT and Departamento de Matemáticas
e-mail
• A. SpivakDepartment of Mathematics
University of California at Berkeley
903 Evans Hall
Berkeley
CA 94720, USA
e-mail

## Search for IMPAN publications

Query phrase too short. Type at least 4 characters.