Hamiltonian approaches of field theory
type: Item
instance of: scholarly article
title: Hamiltonian approaches of field theory
zbMATH Open document ID: 1126.70364
DOI: 10.1155/S0161171204402282
author: Constantin Udrişte
author: Ana-Maria Teleman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/53605
review text: Summary: 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 \(\delta \otimes J\), we prove that the dual action is indefinite, we find the eigenvalues and the eigenfunctions of the operator \((\delta \otimes J)(\partial/\partial t)\) 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.
Mathematics Subject Classification ID: 70S05
Mathematics Subject Classification ID: 70S15
zbMATH DE Number: 2171763
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2171763