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Variational principles and symmetries on fibered multisymplectic manifolds
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) s...
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| Published in: | Communications in Mathematics 2016-12, Vol.24 (2), p.137-152 |
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| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c3157-533961e56a8779db7f5f26f6cfa5a3dd6d3247f1f10b2d6d6392090bb92e87723 |
| container_end_page | 152 |
| container_issue | 2 |
| container_start_page | 137 |
| container_title | Communications in Mathematics |
| container_volume | 24 |
| creator | Gaset, Jordi Prieto-Martínez, Pedro D. Román-Roy, Narciso |
| description | The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics. |
| doi_str_mv | 10.1515/cm-2016-0010 |
| format | article |
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Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. 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| ispartof | Communications in Mathematics, 2016-12, Vol.24 (2), p.137-152 |
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| language | eng |
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| source | Freely Accessible Journals |
| subjects | 49 Calculus of variations and optimal control optimization 49S05 Variational principles of physics 53 Differential geometry 53D Symplectic geometry, contact geometry 55 Algebraic topology 55R Fiber spaces and bundles 70 Mechanics of particles and systems 70S Classical field theories Anàlisi matemàtica Calculus of variations Classificació AMS Conserved quantities Càlcul de variacions Espais fibrats (Matemàtica) Fiber bundles Fiber spaces (Mathematics) Field theory (Physics) Física matemàtica Geometria Geometria computacional Geometria simplèctica Matemàtiques i estadística Mathematics Multisymplectic manifolds Noether theorem Symmetries Symplectic geometry Variational principles Àrees temàtiques de la UPC |
| title | Variational principles and symmetries on fibered multisymplectic manifolds |
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