© Hindawi Publishing Corp. HAMILTONIAN APPROACHES OF FIELD THEORY

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 δ⊗J, we prove that the dual action is indefinite, we find the eigenvalues and the eigenfunctions of the operator (δ⊗J)(∂/∂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 mul-titime 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. 2000 Mathematics Subject Classification: 53C07, 46E20, 55R10