Path-integral formulation of backward and umklapp scattering for 1d spinless fermions

VICTORIA I. FERNÁNDEZ; CARLOS M. NAÓN

THEORETICAL AND MATHEMATICAL PHYSICS

Springer

Año: 1999 vol. 118 p. 385 - 391

0040-5779

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.