Michel theory of symmetry breaking and gauge theories

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 $\mathcal{C}$ of connections of a principal fiber bundle. Our proof follows closely the original one by Michel, using several known results on the geometry of $\mathcal{C}$. The result (and proof) is also extended to the case of gauge theories with matter fields.

24 pages. An old paper posted for archival purposes

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