We determine the effect of a CPT-even and Lorentz violating non-minimal coupling on the differential cross sections for some of the most important tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as electron-positron annihilation. Experimental limits constraining the allowed deviation of the differential cross sections relative to pure QED allow us to place upper bounds on the Lorentz violating parameters. A constraint based on the decay rate of parapositronium is also obtained.

We propose a Gribov-Zwanziger type model action for the Landau-DeWitt gauge that preserves, for any gauge group, the invariance under background gauge transformations. At zero temperature, and to one-loop accuracy, the model can be related to the Gribov no-pole condition. We apply the model to the deconfinement transition in SU(2) and SU(3) Yang-Mills theories and compare the predictions obtained with a single or with various (color dependent) Gribov parameters that can be introduced in the action without jeopardizing its background gauge invariance. The Gribov parameters associated to color directions orthogonal to the background can become negative, while keeping the background effective potential real. In some cases, the proper analysis of the transition requires the potential to be resolved in those regions.