Nonlocal regularization for non-Abelian gauge theories for arbitrary gauge parameter

We study the nonlocal regularization for the non-Abelian gauge theories for an arbitrary value of the gauge parameter xi. We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a xi -independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements (where they exist) independent of xi. (C) 2000 American Institute of Physics. [S0022- 2488(00)02511-1].