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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 100, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.100
(Mi sigma446)
 

This article is cited in 49 scientific papers (total in 49 papers)

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

Narciso Román-Roy

Dept. Matemática Aplicada IV, Edif icio C-3, Campus Norte UPC, C/ Jordi Girona 1, E-08034 Barcelona, Spain
References:
Abstract: This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler–Lagrange and the Hamilton–De Donder–Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Keywords: classical field theories; Lagrangian and Hamiltonian formalisms; fiber bundles; multisymplectic manifolds.
Received: July 2, 2009; in final form October 30, 2009; Published online November 6, 2009
Bibliographic databases:
Document Type: Article
MSC: 70S05; 55R10; 53C80
Language: English
Citation: Narciso Román-Roy, “Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories”, SIGMA, 5 (2009), 100, 25 pp.
Citation in format AMSBIB
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\by Narciso Rom\'an-Roy
\paper Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
\jour SIGMA
\yr 2009
\vol 5
\papernumber 100
\totalpages 25
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  • This publication is cited in the following 49 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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