SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Nov 2007Embargo end date: 01 Jan 2007 Spain English Publisher:World Scientific Pub Co Pte LtJournal:Reviews in Mathematical Physics, volume 19, pages 1,117-1,147 (issn: 0129-055X, eissn: 1793-6659,

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Authors: Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia;

doi: 10.1142/s0129055x07003188 , 10.48550/arxiv.math-ph/0703035

arXiv: math-ph/0703035

handle: 2117/673

SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

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Abstract

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.

Country

Spain

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
University of Santiago de Compostela
Spain
University of Santiago de Compostela (USC)
Spain

Keywords

70S05, 70S10, 53D05, Classificació AMS::53 Differential geometry::53D Symplectic geometry, FOS: Physical sciences, Lagrangian gauge symmetries, Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics, Simetria, Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, Noether theorem, contact geometry, k-symplectic manifolds, :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], Cartan symmetries, Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Conservation laws, Àrees temàtiques de la UPC::Matemàtiques i estadística, Bayesian field theory, Symplectic geometry, :Matemàtiques i estadística [Àrees temàtiques de la UPC], Mathematical Physics (math-ph), Lagrangian and Hamiltonian field theories, :53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], Noether's theorem, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, Varietats simplèctiques, Symmetries and conservation laws in mechanics of particles and systems, conservation laws, Symmetries

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Higher-order Cartan symmetries in k-symplectic field theory
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