Landau-Khalatnikov-Fradkin transformation for the Quark Propagator in an SU(N) Gauge Theory

Abstract

In the framework of the SU(N) gauge field theory, we embark on a comprehensive exploration of the transformation properties of n-point Green functions. Specifically, we center our focus on propagators and vertices, which undergo a coordinated local gauge transformation involving the gluon vector potential and the quark matter field. This transformation ensures the invariance of physical observables, upholding their consistent representation across varied gauge perspectives. Our research delineates the underlying non-perturbative transformation law for the quark propagator in covariant gauges. We advance a meticulous perturbative expansion of this transformation up to Og^6 and extend our calculations to Og^8 for selected terms. Through this study, we unearth significant insights regarding the quark-anti-quark condensate, the multiplicative renormalizability of the quark propagator in its massless state, and its symbiotic relationship with the quark-gluon vertex at a one-loop level. Furthermore, by assigning values of CF = 1 and CA = 0, we discern that the Landau-Khalatnikov- Fradkin transformation can be simplistically mapped to the abelian context seen in quantum electrodynamics.