Schwinger function, confinement, and positivity violation in pure gauge QED

The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement realized as its phase diagram has a confined and deconfined that depends on the value of coupling constant, i.e. $\beta$. Herein, connection between positivity violation through Schwinger function associated with Landau photon propagator investigated. simulations reported show very clear link realization and, therefore, K\"all\'en-Lehmann spectral density. Furthermore, mass scale characterizes decay for small time separations computed used distinguish two phases theory.