Confinement in QED

It is believed that in QCD its fundamental constituints are confined, i.e. that the Hilbertspace of the physics states does not include single quark or gluon states. How thisproperties translates into two point correlation functions is not clear.

Certainly,positivity violation is an indication of confinement. Do we have other theories whereconfinement takes place? Indeed, this happens for the compact formulation on latticeof QED that has two phases: a confined and a non-confined phase.

Then, how do theparticle propagators look like in each phase? What about positivity violation? In orderto help answering these questions, we revist the photon propagator for the puregauge theory.

In the confined case we show that it has an associated linearly growingpotential, it has a mass gap, that is related to the presence of monopoles, and itsspectral function is not positive defined. In the non-confining phase, our simulationssuggest that a free field theory is recovered in the thermodynamic limit.