Geometrical approach to the reduction of gauge theories with spontaneously broken symmetry (Q1069159)

The authors present a geometric description of gauge theories with a Higgs field and associated spontaneous symmetry breaking. For gauge a group G and a subgroup H of G, a Higgs field is a cross section of the fibre bundle with fibre G/H. Then the original G-gauge theory is reduced to an H-gauge theory geometrically, as an application of the reduction theorem for structural groups. The authors give a coordinate description of the reduced subbundle and they show that for gauge equivalent Higgs fields the corresponding subbundles are homeomorphic. For the reduced physical fields they show that initially G-equivalent fields may fail to be H-equivalent after the reduction. The effects of the reductions on the connections are also investigated.