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arXiv · 1508.04632

Lie Groupoids in Classical Field Theory I: Noether's Theorem

Bruno T. Costa·Michael Forger·Luiz Henrique P. Pêgas
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Abstract

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.

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Bruno T. Costa, Michael Forger, Luiz Henrique P. Pêgas. 2015-08-19. Lie Groupoids in Classical Field Theory I: Noether's Theorem. https://arxiv.org/abs/1508.04632

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