Study of a two-dimensional model with axial-current-pseudoscalar derivative interaction

A detailed study is made of a massive pseudoscalar field interacting via derivative coupling with massless fermions in two-dimensional space-time. The model provides an example of a soluble renormalizable theory with an anomalous axial-vector current and a zero-mass particle interpretation for the fermion. Except for a finite mass and wavefunction renormalization, the boson remains free in the presence of the interaction. The canonical fermion field exhibits an anomalous dimension that is found to be in agreement with the asymptotic Callan-Symanzik equation. The connection between the Wilson expansion for defining operator products in this model and the Dyson equations of renormalized perturbation theory is discussed, and agreement with second-order perturbation theory is verified by explicit calculation.