Theory of Classical Higgs Fields. III. Metric-affine gauge theory

TL;DR

This paper develops a classical gauge theory framework incorporating spontaneous symmetry breaking, where Higgs fields are sections of a quotient bundle, exemplified by metric-affine gauge theory with applications to gauge gravitation.

Contribution

It formulates a comprehensive classical gauge theory with spontaneous symmetry breaking on principal bundles, including metric-affine gauge theory with Higgs and matter fields.

Findings

Describes gauge fields as linear connections on manifolds.

Identifies Higgs fields as pseudo-Riemannian metrics.

Applies framework to gauge gravitation theory.

Abstract

We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.