Spontaneous symmetry breaking in the Kaluza-Klein theory

We develop an alternative variant of the transition to the four-dimensional space-time in the Kaluza-Klein theories: instead of averaging over the additional coordinates, we carry out contraction to a four-dimensional submanifold. It is shown that in this approach, in addition to the usual Kaluza-Klein Lagrangian, the total Lagrangian of the theory contains terms which are analogous to the Kiggs terms. This leads to spontaneous breaking of the gage symmetry.