Abelian and non-Abelian bosonization in the path-integral framework

Abstract

Abelian and non-Abelian bosonization of two-dimensional models is discussed within the path-integral framework. Concerning the Abelian case, the equivalence between the massive Thirring and the sine-Gordon models is rederived in a very simple way by making a chiral change in the fermionic path-integral variables. The massive Schwinger model is also studied using the same technique. The extension of this bosonization approach to the solution of non-Abelian models is performed in a very natural way, showing the appearance of the Wess-Zumino functional through the Jacobian associated with the non-Abelian chiral change of variables. Relevant features of massless two-dimensional QCD are discussed in this context.