Nonperturbative Fermion-Boson Vertex Function in Gauge Theories
  The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal (longitudinal) and transverse Ward-Takahashi relations for the The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal(longitudinal) and transverse Ward-Takahashi relations for the fermion-boson and the axial-vector vertices in the case of massless fermion, in which the possible quantum anomalies and perturbative corrections are taken into account simultaneously. We find that this nonperturbative fermion-boson vertex function is expressed nonperturbatively in terms of the full fermion propagator and contains the contributions of the transverse axial anomaly and perturbative corrections. The result that the transverse axial anomaly contributes to the nonperturbative fermion-boson vertex arises from the coupling between the fermion-boson and the axial-vector vertices through the transverse Ward-Takahashi relations for them and is a consequence of gauge invariance. 
Han-xin He