ON THE GEOMETRY OF SPONTANEOUS SYMMETRY-BREAKING

Given a principal bundle P --> X with a structure group G and an associated Higgs bundle SIGMA with a standard fiber G/H, the case of a matter bundle E whose standard fiber admits action only of an exact symmetry subgroup H of G is examined. In the presence of a fixed Higgs field sigma: X --> SIGMA, matter fields are represented by sections of a matter bundle E(h) associated with the corresponding reduced subbundle P(h) of P. The totality of matter fields and Higgs fields is described by sections of the bundle E approximately which is the composite bundle E(H) --> SIGMA --> X where E(H) --> SIGMA is the bundle associated with the principal H-bundle P --> SIGMA. The bundle E fails to be associated with a principal bundle. To construct a connection GAMMA: E approximately --> J1 E approximately on E approximately, the canonical jet bundle morphism J1 E(H) x J1 SIGMA --> J1 E approximately is used.