International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 57, Pages 3045-3056

Hamiltonian approaches of field theory

Constantin Udrişte1 and Ana-Maria Teleman2

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.


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 δJ, we prove that the dual action is indefinite, we find the eigenvalues and the eigenfunctions of the operator (δJ)(/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.