New look at QED4: The photon as a Goldstone boson and the topological interpretation of electric charge

A. Kovner*, Rosenstein Baruch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We develop the dual picture for quantum electrodynamics in 3+1 dimensions. It is shown that the photon is massless in the Coulomb phase due to spontaneous breaking of the magnetic symmetry group. The generators of this group are the magnetic fluxes through any infinite surface 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 operator, the Goldstone theorem is applicable if V(C)0. If the system is properly regularized in the infrared, we find V(C)0 in the Coulomb phase and V(C)=0 in the Higgs phase. The Higgs-Coulomb phase transition is therefore understood as a condensation of magnetic vortices. The electric charge in terms of V(C) is topological and is equal to the winding number of the mapping from a circle at spatial infinity into the manifold of possible vacuum expectation values of a magnetic vortex in a given direction. Since the vortex operator takes values in S1 and 1(S1)=Z, the electric charge is quantized topologically.

Original languageEnglish
Pages (from-to)5571-5581
Number of pages11
JournalPhysical Review D
Volume49
Issue number10
DOIs
StatePublished - 1 Jan 1994

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