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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| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| ISSN: | 1815-0659 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.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
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862688025045106688 |
|---|---|
| author | Román-Roy, N. |
| author_facet | Román-Roy, N. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T16:07:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149096 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:07:48Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Román-Roy, N. 2019-02-19T17:19:11Z 2019-02-19T17:19:11Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149096 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. I acknowledge the financial support of Ministerio de Educaci´on y Ciencia, projects MTM 2005–04947, MTM 2008–00689/MTM and MTM 2008–03606–E/MTM. I wish to thank to Professors Miguel C. Mu˜noz-Lecanda and Xavier Gr`acia for their comments, and to the referees, whose suggestions have allowed me to improve this work. Finally, thanks also to Mr. Jef f Palmer for his assistance in preparing the English version of the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Article published earlier |
| spellingShingle | Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories Román-Roy, N. |
| title | 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_short | Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories |
| title_sort | multisymplectic lagrangian and hamiltonian formalisms of classical field theories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149096 |
| work_keys_str_mv | AT romanroyn multisymplecticlagrangianandhamiltonianformalismsofclassicalfieldtheories |