How to get masses from Kaluza-Klein theory (Q910033)

Starting off with a principal fibre bundle P equipped with an invariant Lorentzian metric g, the authors analyze symmetry breaking by considering the vertical part of the metric as a Higgs field, the values of which are constrained to an orbit of the symmetry group. This results in a splitting of the gauge field into a residual Yang-Mills field and massive vector bosons. Furthermore, an Einstein type field equation for the metric g and its splitting into ordinary Einstein equation, Yang-Mills equation, and Klein-Gordon type equation, is discussed. The general theory is illustrated by an example where the symmetry group Spin(4) is broken to U(1).