Anomalous properties of vector currents in exactly solvable field theory models

A study is made of the anomalous properties of the vector and axial currents in two exactly solvable field theory models in a two-dimensional space-time. The models are the interaction of a massless fermion with external vector and axial fields and the current-current interaction of two different massless fermions. The method proposed previously by the author (Teor. Mat. Fiz., 3, 220 (1970)) is used to eliminate the indeterminacy of the models. Both models are constructed unambiguously. The Heisenberg operators of the fields and currents are found. It is shown that the axial current is not conserved in the first model. In the second model, the vector current of one fermion does not commute at equal times with the field operators of the other fermion, although the field operators satisfy the canonical anticommutation relations.