Michel theory of symmetry breaking and gauge theories

TL;DR

This paper generalizes Michel's theorem on symmetry breaking to pure gauge theories and those with matter fields, using geometric methods to analyze gauge-invariant functionals on connection spaces.

Contribution

It extends Michel's symmetry breaking theorem to gauge theories, incorporating matter fields and utilizing geometric analysis of connection spaces.

Findings

Extension of Michel's theorem to pure gauge theories

Inclusion of matter fields in the symmetry breaking analysis

Geometric proof based on the space of connections

Abstract

We extend Michel's theorem on the geometry of symmetry breaking [L. Michel, {\it Comptes Rendus Acad. Sci. Paris} {\bf 272-A} (1971), 433-436] to the case of pure gauge theories, i.e. of gauge-invariant functionals defined on the space ${\cal C}$ of connections of a principal fiber bundle. Our proof follows closely the original one by Michel, using several known results on the geometry of ${\cal C}$. The result (and proof) is also extended to the case of gauge theories with matter fields.