Extended BRS Symmetry and Gauge Independence in On-Shell Renormalization   Schemes
  Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant $Z_2$ in on-shell QED renormalization schemes. A necessary condition for gauge independence of $Z_2$ in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD. 
S. Alavian and T.G. Steele