It is believed that in QCD its fundamental constituents are confined, i.e. that the Hilbert space of the physical states does not include single quark or gluon states. How this property translates into two point correlation functions is not clear. Certainly, positivity violation is an indication of confinement. Do we have other theories where confinement takes place? Indeed, this happens for the compact formulation of QED on the lattice that has two phases: a confined and a non-confined phase. Then, how do the particle propagators look like in each phase? What about positivity violation? In order to help answering these questions, we revisit the photon propagator for the pure gauge theory. In the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function is not positive defined. In the non-confining phase, our simulations suggest that a free field theory is recovered in the thermodynamic limit.
Paulo Brás, Paulo Silva, Jaime Silva