Covariant Hamiltonian Field Theories on Manifolds with Boundary:
  Yang-Mills Theories

There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

Abstract

The multisymplectic formalism for first order covariant Hamiltonian field theories on manifolds with boundary is described and a general geometric formalism for the theory of boundary conditions based on the preservation of the conservation laws along the boundary is presented. This approach provides a natural geometrical realization of Fock's description of field theories as used for instance in recent work by Cattaneo, Mnev and Reshetikhin [Ca14]. The notions of the theory will be tested against three significant examples: scalar fields, Poisson sigma model and Yang-Mills theories.