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Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory
Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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