A new Lagrangian dynamic reduction in field theory
Mathematical Physics
2014-07-02 v1 math.MP
Abstract
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
Cite
@article{arxiv.1407.0263,
title = {A new Lagrangian dynamic reduction in field theory},
author = {François Gay-Balmaz and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:1407.0263},
year = {2014}
}
Comments
This paper has appeared in 2010 in the Annales de l'Institut Fourier 16(3), 1125-1160