Symmetries in Lagrangian Field Theory

By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first order jet bundles \(J^1\pi\)...

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Bibliographic Details
Published in:arXiv.org 2015-02
Main Authors: Búa, Lucía, Bucataru, Ioan, de León, Manuel, Salgado, Modesto, Vilariño, Silvia
Format: Article
Language:English
Subjects:
Field theory
Independent variables
Time dependence
Online Access:Get full text
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Summary:By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first order jet bundles \(J^1\pi\) of a fiber bundle \(\pi:E\to {\mathbb R}^k\) where \({\mathbb R}^k\) is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.
ISSN:2331-8422
DOI:10.48550/arxiv.1403.5397