Relating Calculations and Renormalization in Axial and Lorentz Gauges and Gauge-independence

We study futher the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the 1-loop approximation for the wavefunction renormalization and the identity of the beta-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the 1-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave-function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the beta functions in the two gauges.