Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Look at QED$_4$: the Photon as a Goldstone Boson and the Topological
  Interpretation of Electric Charge   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 $\Phi_S$. 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 operator, the Goldstone theorem is applicable if $<V(C)>\ne
0$. If the system is properly regularized in the infrared, we find $<V(C)>\ne
0$ in the Coulomb phase and $V(C)=0$ in the Higgs phase. The Higgs - Coulomb
phase transition is therefore understood as 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 $S^1$ and
$\Pi_1(S^1)={\cal Z}$, the electric charge is quantized topologically.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn