Open Access
VOL. 5 | 2004 On Phase Spaces and the Variational Bicomplex
Enrique G. Reyes

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2004: 189-202 (2004) DOI: 10.7546/giq-5-2004-189-202


The notion of a phase space in classical mechanics is of course well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous propositions for such a generalization have appeared in the literature. In this contribution we review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau’s symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the variational bicomplex. We present a basic example, and briefly discuss some possible avenues of research.


Published: 1 January 2004
First available in Project Euclid: 12 June 2015

zbMATH: 1065.37046
MathSciNet: MR2082304

Digital Object Identifier: 10.7546/giq-5-2004-189-202

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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