Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
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 usi...
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National Academy of Science of Ukraine
2009-11-01
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doaj-bb3fb72abb2544bab6d62518a6480f632020-11-25T01:50:29ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-11-015100Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field TheoriesNarciso Román-RoyThis 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.http://dx.doi.org/10.3842/SIGMA.2009.100classical field theoriesLagrangian and Hamiltonian formalismsfiber bundlesmultisymplectic manifolds |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Narciso Román-Roy |
spellingShingle |
Narciso Román-Roy Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Symmetry, Integrability and Geometry: Methods and Applications classical field theories Lagrangian and Hamiltonian formalisms fiber bundles multisymplectic manifolds |
author_facet |
Narciso Román-Roy |
author_sort |
Narciso Román-Roy |
title |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
title_short |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
title_full |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
title_fullStr |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
title_full_unstemmed |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
title_sort |
multisymplectic lagrangian and hamiltonian formalisms of classical field theories |
publisher |
National Academy of Science of Ukraine |
series |
Symmetry, Integrability and Geometry: Methods and Applications |
issn |
1815-0659 |
publishDate |
2009-11-01 |
description |
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. |
topic |
classical field theories Lagrangian and Hamiltonian formalisms fiber bundles multisymplectic manifolds |
url |
http://dx.doi.org/10.3842/SIGMA.2009.100 |
work_keys_str_mv |
AT narcisoromanroy multisymplecticlagrangianandhamiltonianformalismsofclassicalfieldtheories |
_version_ |
1725001639754989568 |