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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Published in:arXiv.org 2015-02
Main Authors: Búa, Lucía, Bucataru, Ioan, de León, Manuel, Salgado, Modesto, Vilariño, Silvia
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Language:English
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Field theory
Independent variables
Time dependence
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Bucataru, Ioan
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Salgado, Modesto
Vilariño, Silvia
description 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.
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subjects Field theory
Independent variables
Time dependence
title Symmetries in Lagrangian Field Theory
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