Functional integral approach of the two-dimensional massive fermion model with Thirring interaction among different species

Abstract

We use the Abelian reduction of the Wess–Zumino–Witten theory to perform the functional integral bosonization of the two-dimensional fermion model with Thirring interaction among N different massive Fermi field species. The operator solution for the quantum equations of motion is reconstructed from the functional integral formulation. The fermion–boson correspondences, obtained earlier by Halpern, are generalized to the case of quartic interaction between different Fermi field species. For the massless model, the general Wightman functions of the Fermi field are displayed. The partition function and the equation of state of the statistical mechanical system associated with the effective bosonized theory are obtained. The charge screening mechanism for the Thirring field is discussed by considering the model with local gauge symmetry. The present approach provides a general guideline in order to obtain the operator solution of two-dimensional Abelian models, since we only need to know the free-field fermion–boson correspondences in order to reconstruct from the functional integral formulation the operator solution for the quantum equations of motion.