Cm. Naon et al., FIELD-THEORETICAL APPROACH TO NONLOCAL INTERACTIONS - 1D ELECTRONS AND FERMIONIC IMPURITIES, Nuclear physics. B, 485(3), 1997, pp. 665-684
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.