Structural aspects of functional integral bosonization
L. V. Belvedere · Journal of Physics A Mathematical and General · 2000
We discuss structural aspects of functional integral bosonization of two-dimensional models. We show that the use of auxiliary vector fields enlarges the Hilbert space by the introduction of an external field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. These aspects are discussed in a model with well known and established results in the literature, by considering the Abelian reduction 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 Thirring and sine-Gordon theories. We show that the factorization of the partition function will generally lead to incorrect conclusions concerning the physical content of the model, such as the existence of infinitely delocalized states and the violation of the asymptotic factorization property of the Wightman functions. In order to exert control on the effect of the redundant Bose fields and obtain the fermion-boson mapping in the Hilbert space of states, the functional integral bosonization must be performed on the generating functional.