Hamiltonian approaches of field theory

Constantin Udrişte and Ana-Maria Teleman

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

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 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:837534

DOI: 10.1155/S0161171204402282

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