Proceedings of the International Conference on Geometry, Integrability and Quantization

On Phase Spaces and the Variational Bicomplex

Enrique G. Reyes

Abstract

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.

Article information

Source
Proceedings of the Fifth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Allen C. Hirshfeld, eds. (Sofia: Softex, 2004), 189-202

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1434147927

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

Mathematical Reviews number (MathSciNet)
MR2082304

Zentralblatt MATH identifier
1065.37046

Citation

Reyes, Enrique G. On Phase Spaces and the Variational Bicomplex. Proceedings of the Fifth International Conference on Geometry, Integrability and Quantization, 189--202, Softex, Sofia, Bulgaria, 2004. doi:10.7546/giq-5-2004-189-202. https://projecteuclid.org/euclid.pgiq/1434147927


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