In [1] Kenneth G. Wilson proposed a mechanism for confinement using lattice paths what leds him to the concept of Wilson loop. It seems to me that he is using mainly a single abelian field. He says

The model discussed in this paper is a single Abelian gauge field coupled (with strength g) to massive quarks. In weak coupling the gauge field behaves like a normal free zero-mass field (despite modifications introduced in the lattice quantization) and the quarks are unbound. In strong coupling the gauge field is massive and the quarks are bound, showing the existence of the second phase

Despite he never uses the word "QED" I think that his model would show that there is a confining phase in QED at strong coupling. But it is not clear to me if the potential between sources in an abelian gauge field theory must be always a Coulomb type.

From my knowledge what we want is a theory describing the confinement and deconfined phases, at least for QCD, or not?

Is the mechanism proposed by Wilson predicting that QED has a confining phase?

[1] Kenneth G. Wilson; Confinement of Quarks; Phys.Rev. D10 (1974) 2445-2459

  • $\begingroup$ Indeed, strongly coupled compact QED confines and weakly coupled does not.; there is a phase transition between these two regimes. Generalization to nonabelian groups such as SU(2) and SU(3) indicates a similarly confining strong coupling regime, without a phase boundary separating it from the weak coupling regime. $\endgroup$ May 30, 2018 at 19:09
  • $\begingroup$ @CosmasZachos thank you, how is that related to Wilson's paper? I'm not sure if he is talking about compact qed when he said "...is a single abelian model...". Do you know which paper inroduced compact QED for the first time? $\endgroup$ Jun 1, 2018 at 2:05
  • $\begingroup$ This Is compact lattice QED! $\endgroup$ Jun 1, 2018 at 2:45

1 Answer 1


If you use lattice formalism of gauge theory, defining all that Wilson action and related objects, you can obtain asymptotic form of the potential by calculating the expectation value of Wilson loop. Then for strong coupling limit (where we do strong coupling expansion), even in QED(single abelian or U(1)), you get linearly rising term.

However in weak coupling phase, (inverse coupling larger than 1.01) this term vanishes.

I'm not sure if it has physical meaning or just an lattice phenomenon. I was just about to study the subject. This paper might help both of us. Kondo, Phys.Rev. D58 (1998) 085013


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