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arXiv · 1405.2249

Slice theorem for Fréchet group actions and covariant symplectic field theory

Tobias Diez
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Abstract

A general slice theorem for the action of a Fréchet Lie group on a Fréchet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The presented slice theorem is illustrated by its application to gauge theories: the action of the gauge transformation group admits smooth slices at every point and thus the gauge orbit space is stratified by Fréchet manifolds. Furthermore, a covariant and symplectic formulation of classical field theory is proposed and extensively discussed. At the root of this novel framework is the incorporation of field degrees of freedom F and spacetime M into the product manifold F * M. The induced bigrading of differential forms is used in order to carry over the usual symplectic theory to this new setting. The examples of the Klein-Gordon field and general Yang-Mills theory illustrate that the presented approach conveniently handles the occurring symmetries.

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Tobias Diez. 2014-05-09. Slice theorem for Fréchet group actions and covariant symplectic field theory. https://arxiv.org/abs/1405.2249

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