  We use the radial gauge to calculate the recently proposed ansatz for the
physical electron propagator in such effective models of strongly correlated
electron systems as the $QED_3$ theory of the pseudogap phase of the cuprates.
The results of our analysis help to settle the recent dispute about the sign
and the magnitude of the anomalous dimension which characterizes the gauge
invariant amplitude in question and set the stage for computing other, more
physically relevant, ones.
