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We develop the dual picture for Quantum Electrodynamics in 3+1 dimensions. Itis shown that the photon is massless in the Coulomb phase due to spontaneousbreaking of the magnetic symmetry group. The generators of this group are themagnetic fluxes through any infinite surface $\Phi_S$. The order parameter forthis symmetry breaking is the operator $V(C)$ which creates an infinitely longmagnetic vortex. We show that although the order parameter is a stringlikerather than a local operator, the Goldstone theorem is applicable if $<V(C)>\ne0$. If the system is properly regularized in the infrared, we find $<V(C)>\ne0$ in the Coulomb phase and $V(C)=0$ in the Higgs phase. The Higgs - Coulombphase transition is therefore understood as condensation of magnetic vortices.The electric charge in terms of $V(C)$ is topological and is equal to thewinding number of the mapping from a circle at spatial infinity into themanifold of possible vacuum expectation values of a magnetic vortex in a givendirection. Since the vortex operator takes values in $S^1$ and$\Pi_1(S^1)={\cal Z}$, the electric charge is quantized topologically.Comment: 24 pages, latex. 3 figures available on request. LA-UR-92-347

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

New look at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">QED</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>: the photon as a Goldstone boson and the topological interpretation of electric charge

New look atQED4: the photon as a Goldstone boson and the topological interpretation of electric charge