Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theor...

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Detalhes bibliográficos
Autores: Román Roy, Narciso|||0000-0003-3663-9861, Salgado, Modesto, Vilariño, Silvia
Formato: artículo
Fecha de publicación:2007
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/673
Acesso em linha:https://hdl.handle.net/2117/673
Access Level:acceso abierto
Palavra-chave:Symplectic geometry
Bayesian field theory
Symmetries
Conservation laws
Noether theorem
Lagrangian and Hamiltonian field theories
k-symplectic manifolds
Varietats simplèctiques
Simetria
Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descrição
Resumo:This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.