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 ξ. 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 ξ-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 ξ. 1.INTRODUCTION Local Quantum Field Theories are plagued with infinities and need regularization to make the process of renormalization mathematically well-defined. Many regularizations have been proposed over the last 50 years, dimensional regularization being one used widest due to its effectiveness[1]. While dimensional regularization is useful in a wide class of Quantum Field Theories, it cannot be used directly in Supersymmetric Field Theories. A number of regularizations have been proposed over the last decade that can be used in Supersymmetric Field Theories[2,3]. Nonlocal regularization is one of them[2, 4, 5]. Nonlocal regularization proposed by Evans et al[2] has been extensively studied[4, 5, 6]. Renormalization procedure has been established upto two