  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.
