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arXiv · 1407.0263

A new Lagrangian dynamic reduction in field theory

François Gay-Balmaz·Tudor S. Ratiu
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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.

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François Gay-Balmaz, Tudor S. Ratiu. 2014-07-01. A new Lagrangian dynamic reduction in field theory. https://arxiv.org/abs/1407.0263

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