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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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149096 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories / N. Román-Roy // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 98 назв. — англ. |
Репозитарії
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irk-123456789-1490962019-02-20T01:26:31Z Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Román-Roy, N. 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. 2009 Article Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories / N. Román-Roy // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 98 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70S05; 55R10; 53C80 http://dspace.nbuv.gov.ua/handle/123456789/149096 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Román-Roy, N. |
| spellingShingle |
Román-Roy, N. Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Román-Roy, N. |
| author_sort |
Román-Roy, N. |
| 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 |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149096 |
| citation_txt |
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories / N. Román-Roy // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 98 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT romanroyn multisymplecticlagrangianandhamiltonianformalismsofclassicalfieldtheories |
| first_indexed |
2023-05-20T17:32:08Z |
| last_indexed |
2023-05-20T17:32:08Z |
| _version_ |
1796153519688908800 |