  We present a (1+1)-dimensional fermionic QFT with non-local couplings between
currents. This model describes an ensemble of spinless fermions interacting
through forward, backward and umklapp scattering processes. We express the
vacuum to vacuum functional in terms of a non trivial fermionic determinant.
Using path-integral methods we find a bosonic representation for this
determinant. Thus we obtain an effective action depending on three scalar
fields, two of which correspond to the physical collective excitations whereas
the third one is an auxiliary field that is left to be integrated by means of
an approximate technique.
