FIELD-THEORETICAL APPROACH TO NONLOCAL INTERACTIONS - 1D ELECTRONS AND FERMIONIC IMPURITIES

We apply a recently proposed path-integral approach to non-local boson ization to a Thirring-like system modeling non-relativistic massless p articles interacting with localized fermionic impurities. We consider forward-scattering processes described by symmetric potentials includi ng interactions between charge, current, spin and spin-current densiti es. In the general (spin-flipping) problem we obtain an effective acti on 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 exp ressions for the dispersion relations of collective modes and two-poin t fermionic correlation functions as functionals of the potentials. Fi nally, as an example, we compute the momentum distribution for the cas e 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 Ferm i liquid behavior.