Hamiltonian approaches of field theory (Q1777830)

Summary: We extend some results and concepts of single-time covariant Hamiltonian field theory to the new context of multitime covariant Hamiltonian theory. In this sense, we point out the role of the polysymplectic structure \(\delta \otimes J\), we prove that the dual action is indefinite, we find the eigenvalues and the eigenfunctions of the operator \((\delta \otimes J)(\partial/\partial t)\) with periodic boundary conditions, and we obtain interesting inequalities relating functionals created by the new context. As an important example for physics and differential geometry, we study the multitime Yang-Mills-Witten Hamiltonian, extending the Legendre transformation in a suitable way. Our original results are accompanied by well-known relations between Lagrangian and Hamiltonian, and by geometrical explanations regarding the Yang-Mills-Witten Lagrangian.