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Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
Інший ID:
2000 Mathematics Subject Classification: 70S05; 55R10; 53C80
Посилання:
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.
Підтримка:
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.
Дата:
2009
Переглядів:
260
Завантажень:
147
Анотація:
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.
