Gauge reduction in covariant field theory

Abstract

In this work we develop a Lagrangian reduction theory for covariant field theories with local symmetries and, more specifically, with gauge symmetries. We model these symmetries by using a Lie group fiber bundle acting fiberwisely on the corresponding configuration bundle. In order to reduce the variational principle, we utilize generalized principal connections, a type of Ehresmann connections that are equivariant by the fiberwise action. After obtaining the reduced equations, we give the reconstruction condition and we relate the vertical reduced equation with the Noether theorem. Lastly, we illustrate the theory by applying it to several examples, including the classical case (Lagrange-Poincaré reduction) and electromagnetism.