International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57, Pages 3045-3056
doi:10.1155/S0161171204402282
Hamiltonian approaches of field theory
1Department of Mathematics I, University Politehnica of Bucharest, Splaiul Independenţei 313, Bucharest 060042, Romania
2Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, Bucharest 70109, Romania
Received 18 February 2004
Copyright © 2004 Constantin Udrişte and Ana-Maria Teleman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.