Theory of Classical Higgs Fields. I. Matter Fields

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 $G$.