  Higgs fields are attributes of classical gauge theory on a principal bundle
$P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup
$H$. They are represented by sections of the quotient bundle $P/H\to X$. A
problem lies in description of matter fields with an exact symmetry group $H$.
They are represented by sections of a composite bundle which is associated to
an $H$-principal bundle $P\to P/H$. It is essential that they admit an action
of a gauge group $G$.
