Path-integral bosonization of a non-local interaction and its application to the study of 1d many-body systems

Abstract

We extend the path-integral approach to bosonization to the case in which the fermionic interaction is non-local. In particular we obtain a completely bosonized version of a Thirring-like model with currents coupled by general (symmetric) bilocal potentials. The model contains the Tomonaga-Luttinger model as a special case; exploiting this fact we study the basic properties of the 1d spinless fermionic gas: fermionic correlators, the spectrum of collective modes, etc. Finally, we discuss the generalization of our procedure to the non-abelian case, thus providing a new tool to be used in the study of 1d many-body systems with spin-flipping interactions.