Gauge Fixing Identity in the Background Field Method of QCD in Pure Gauge

Abstract

In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in $Z[A,J,\eta ,\bar{\eta }]$ in the background field method of QCD in pure gauge. Using this gauge fixing identity we establish a relation between $Z[J,\eta ,\bar{\eta }]$ in QCD and $Z[A,J,\eta ,\bar{\eta }]$ in background field method of QCD in pure gauge. We show the validity of this gauge fixing identity in general non-covariant and general Coulomb gauge fixings respectively. This gauge fixing identity is used to prove factorization theorem in QCD at high energy colliders and in non-equilibrium QCD at high energy heavy-ion colliders.

Comments: 14 pages latex, Non-covariant gauge fixing added, (Accepted for Publication in IJMPA)