THE OPERATOR PRODUCT EXPANSION OF THE QCD PROPAGATORS

Abstract

We bring together for the first time the coefficients in covariant gauges of all the condensates of dimension four or less in the operator product expansion (OPE) of the quark, gluon and ghost propagators. It is stressed that contrary to general belief the condensates do not enter the OPE of the propagators in gauge-invariant combinations like [Formula: see text] and 〈G2〉. The results are presented in arbitrary dimension to lowest order in the light quark masses for the SU (Nc) internal symmetry group. All terms which, through the equations of motion, may be viewed as being effectively of order αs are included. The importance of the equations of motion if one is to fulfill the Slavnov-Taylor identities is demonstrated. We briefly consider the equivalent, but less complete, calculations in other gauges and give an overview of the status of the OPE of the QCD vertices. Finally we discuss what these non-perturbative structures tell us about the correct solutions of QCD and point out their significance for the Fourier acceleration technique as applied to lattice QCD.