DYNAMICAL GAUGE FIELD-INDUCED BY THE BERRY PHASE MECHANISM

Some part of the local gauge symmetries in the low energy region, say, lower than GUT or the Planck energy, can be an induced symmetry that can be described with the holonomy fields associated with a topologically nontrivial structure of partially compactified space. In the case where a six-dimensional space is compactified by the Kaluza-Klein mechanism into a product of the four-dimensional Minkowski space M4 and a two-dimensional Riemann surface with the genus g, Sigma(g), we show that, in a limit where the compactification mass scale is sent to infinity, a model Lagrangian with a U(1) gauge symmetry produces the dynamical gauge fields in M4 with a product of g U(1)'s symmetry, i.e. U(1)X...XU(1). These fields are induced by a Berry phase mechanism, not by the Kaluza-Klein mechanism. The dynamical degrees of freedom of the induced fields are shown to come from the holonomies, or the solenoid potentials, associated with the cycles of Sigma(g). The production mechanism of kinetic energy terms for the induced fields is discussed in detail.