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 lin...

We study the one–loop renormalization of noncommutative U (N) gauge theories without matter. We find that for N > 1 the renormalization of the four-point function requires a counterterm which is not present in ordinary gauge theories and breaks the noncommutative gauge invariance. This counterterm is reminiscent of a nonplanar contribution in string theory.