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

@article{Ibort2015CovariantHF, title={Covariant Hamiltonian Field Theories on Manifolds with Boundary: Yang-Mills Theories}, author={Alberto Ibort and Amelia Spivak}, journal={arXiv: Mathematical Physics}, year={2015} }

The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first order covariant Hamiltonian field theories on manifolds with boundaries. This work is a geometric fulfillment of Fock's characterization of field theories as it appears in recent work by Cattaneo, Mnev and Reshetikhin [Ca14]. This framework leads to a true…

## 18 Citations

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We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories,…

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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…

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In the setting of a multisymplectic formalism for Hamiltonian theories on manifolds with boundary a class of admissible boundary conditions based on the principle of preservation of the gauge…

### Covariant reduction of classical Hamiltonian Field Theories: From D’Alembert to Klein–Gordon and Schrödinger

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A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction…

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