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

Department of Mathematics I, University Politehnica of Bucharest, Splaiul Independenţei 313, Bucharest 060042, Romania

Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, Bucharest 70109, Romania

Received 18 February 2004

Copyright © 2004 Hindawi Publishing Corporation. 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 covariantHamiltonian field theory to the new context of multitimecovariant Hamiltonian theory. In this sense, we point out the roleof the polysymplectic structure δ⊗J, we prove thatthe dual action is indefinite, we find the eigenvalues and theeigenfunctions of the operator δ⊗J∂-∂twith periodic boundary conditions, and we obtain interestinginequalities relating functionals created by the new context. Asan important example for physics and differential geometry,we study the multitime Yang-Mills-Witten Hamiltonian, extending theLegendre transformation in a suitable way. Our original resultsare accompanied by well-known relations between Lagrangian andHamiltonian, and by geometrical explanations regarding theYang-Mills-Witten Lagrangian.

Author: Constantin Udrişte and Ana-Maria Teleman

Source: https://www.hindawi.com/


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