  We propose a dynamical mechanism to induce gauge fields in four dimensional
space-time from a single scalar field or a spinor field in higher dimensions.
The Born-Oppenheimer treatment of the extra dimensions is an essential
ingredient in our approach. A possible applications of the idea to low
dimensional condensed matter systems and high temperature field theory are also
pointed out. This paper is an extended version of our previous unpublished work
  (SUNY-NTG-89-48, Jan. 1990).
