Fermion renormalized vertex functions, effective mass, and condensate in an external Yang-Mills gauge field

We investigate the renormalized fermion-gluon vertex, the fermion effective mass, and the fermion condensate when the fermion propagates in an external Yang-Mills gauge field. We use an exact Green’s function for the Dirac operator in a non-Abelian plane-wave gauge field to construct the renormalized vertex function, calculate the on-shell fermion self-energy, and the background-dependent condensate. We consider both the background and operator fields in the axial gauge $k^{\mu }{\mathcal{A}}_{\mu }^a=0$, thereby preserving the gauge. Its applications to strong-field QCD and non-Abelian Schwinger physics are discussed.