|
This article is cited in 47 scientific papers (total in 47 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
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
Citation:
Narciso Román-Roy, “Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories”, SIGMA, 5 (2009), 100, 25 pp.
Linking options:
https://www.mathnet.ru/eng/sigma446 https://www.mathnet.ru/eng/sigma/v5/p100
|
Statistics & downloads: |
Abstract page: | 307 | Full-text PDF : | 84 | References: | 48 |
|