Structural aspects of functional integral bosonization

We discuss structural aspects of functional integral bosonization of two-di mensional models. We show that the use of auxiliary vector fields enlarges the Hilbert space by the introduction of an external field algebra that sho uld not be considered as an element of the intrinsic algebraic structure de fining the model. These aspects are discussed in a model with well known an d established results in the literature, by considering the Abelian reducti on of the Wess-Zumino-Witten theory to reconstruct in the Hilbert space of states Coleman's proof of the fermion-boson mapping between the massive Thi rring and sine-Gordon theories. We show that the factorization of the parti tion function will generally lend to incorrect conclusions concerning the p hysical content of the model, such as the existence of infinitely delocaliz ed states and the violation of the asymptotic factorization property of the Wightman functions. Ln order to exert control on the effect of the redunda nt Bose fields and obtain the fermion-boson mapping in the Hilbert space of states, the functional integral bosonization must be performed on the gene rating functional.