  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.
