NEW LOOK AT QED4 - THE PHOTON AS A GOLDSTONE BOSON AND THE TOPOLOGICAL INTERPRETATION OF ELECTRIC CHARGE

We develop the dual picture for quantum electrodynamics in 3 + 1 dimen sions. It is shown that the photon is massless in the Coulomb phase du e to spontaneous breaking of the magnetic symmetry group. The generato rs of this group are the magnetic fluxes through any infinite surface PHI(S). The order parameter for this symmetry breaking is the operator V(C), which creates an infinitely long magnetic vortex. We show that although the order parameter is a stringlike rather than a local opera tor, the Goldstone theorem is applicable if [V(C)] not-equal 0. If the system is properly regularized in the infrared, we find [V(C)] not-eq ual 0 in the Coulomb phase and [V(C)] = 0 in the Higgs phase. The Higg s-Coulomb phase transition is therefore understood as a condensation o f magnetic vortices. The electric charge in terms of V(C) is topologic al and is equal to the winding number of the mapping from a circle at spatial infinity into the manifold of possible vacuum expectation valu es of a magnetic vortex in a given direction. Since the vortex operato r takes values in S1 and PI1 (S1) = Z, the electric charge is quantize d topologically.