Variational principles and symmetries on fibered multisymplectic manifolds

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/101999

Title:	Variational principles and symmetries on fibered multisymplectic manifolds
Author:	Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Càlcul de variacions -Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica -Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria -Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional -Field theory (Physics) -Calculus of variations -Symplectic geometry -Fiber spaces (Mathematics) -Variational principles -Symmetries -Conserved quantities -Noether theorem -Fiber bundles -Multisymplectic manifolds -Física matemàtica -Anàlisi matemàtica -Geometria simplèctica -Espais fibrats (Matemàtica) -Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories -Classificació AMS::49 Calculus of variations and optimal control; optimization::49S05 Variational principles of physics -Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry -Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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