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 1-d 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 1-d many-body systems with spin-flipping interactions.

We apply a recently proposed path-integral approach to non-local bosonization to a Thirring-like system modeling non-relativistic massless particles interacting with localized fermionic impurities. We consider forward scattering processes described by symmetric potentials including interactions between charge, current, spin and spin-current densities. In the general (spin-flipping) problem we obtain an effective action for the collective modes of the model at T = 0, containing WZW-type terms. When spin-flipping processes are disregarded the structure of the action is considerably simplified, allowing us to derive exact expressions for the dispersion relations of collective modes and two point fermionic correlation functions as functionals of the potentials. Finally, as an example, we compute the momentum distribution for the case in which electrons and impurities are coupled through spin and spin-current densities only. The formulae we get suggest that our formalism could be useful in order to seek for a mechanism able to restore Fermi liquid behavior.

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Chiral gauge theories are studied with a special emphasis on the treatment of gauge degrees of freedom so as to obtain a gauge-invariant effective action from which current commutators can be evaluated. It is explicitly shown in a simple example that these commutators are those to be expected in a gauge-invariant theory.

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