On consistent gauge-fixing conditions in polymerized gravitational systems (Stefan Weigl, FAU) FAU^2 Talk

Gauge fixing is a standard method for deriving the physical sector of a gauge theory. In the context of symmetry reduced models of loop quantum gravity a polymerisation has been applied to gauge fixed models to obtain so called effective theories that mimic the underlying quantum theory to some extend. Motivated from the question whether gauge fixing and polymerization commute, in this talk we will discuss the subtleties of implementing dynamical consistent gauge fixings in the effective theory and present a procedure to determine in a given model the effective lapse and shift. Although we can proof for a range of models that gauge fixing and polymerization does indeed commute and discuss consequences, for most models in the literature this is not the case. We further discuss how for a given choice of effective lapse and/or shift one can obtain a corresponding gauge fixing condition and show that in general this requires non-standard polymerisations or gauge fixing conditions with different classical limits.