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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/673 |
| Acceso en línea: | https://hdl.handle.net/2117/673 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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