Gauge Covariance of the Gap Equation: From the Rainbow Truncation to Gauge Symmetry Constraints

Abstract

The gauge covariance of the quark gap equation is compared for the case of three different quark–gluon vertices: the bare vertex, a Ball–Chiu-like vertex constrained by the corresponding Slavnov–Taylor identity, and a full vertex including the transverse components derived from transverse Slavnov–Taylor identities. The covariance properties are verified with the chiral quark condensate and the pion decay constant in the chiral limit.