SPONTANEOUS BREAKING OF MAGNETIC FLUX SYMMETRY AND DUAL TRANSFORMATION IN (2 + 1)-DIMENSIONAL ELECTRODYNAMICS WITH FOUR-FERMI COUPLING

We consider a class of four-fermi theories in 2 + 1 dimensions minimally coupled to electromagnetism. The low energy effective Lagrangian is derived in the Coulomb phase using a duality transformation. It is shown that the photon field (which is a Goldstone boson following from spontaneous breakdown of the magnetic flux symmetry) plays the same role as any other Goldstone boson, namely that of one of the coordinates on the order parameter manifold. Treating this Lagrangian as a quantum theory, we find that it shows the same phase structure as the original theory, giving thereby the description of the same phases and excitations in the dual language.