Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields
type: Item
instance of: scholarly article
title: Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields
zbMATH Open document ID: 0885.53028
DOI: 10.1016/0393-0440(95)00053-4
published in: Journal of Geometry and Physics
publication date: 1998-04-02T00:00:00Z
review text: A covariant Hamiltonian formulation of field theories is based -- in direct generalization of the symplectic form in classical mechanics -- on a vector-valued two-form, called ``polysymplectic form''. This article uses the natural polysymplectic (``n-symplectic'') structure on frame bundles (given by the exterior derivative of the soldering form) to derive via associated bundles the polysymplectic and multisymplectic structures of Hamiltonian mechanics and field theories. Thus the frame bundle can be considered as a universal polysymplectic bundle. The construction of the symplectic structure in mechanics and the multisymplectic structure on the affine cojet bundle (as used in the ``GIMMSY'' project) are explicitly worked out.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70Sxx
zbMATH DE Number: 951813
zbMATH Keywords: polysymplectic
zbMATH Keywords: multisymplectic
zbMATH Keywords: Hamiltonian field theory
zbMATH Keywords: frame bundle
author: Ronald O. Fulp
author: Jeffrey K. Lawson
author: L. K. Norris
reviewed by: Christian Günther
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00053-4
OpenAlex ID: W2042449037
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Wikidata QID: Q128133413
description: scientific article; zbMATH DE number 951813