Non-local Thirring model with backward and umklapp interactions

Abstract

We extend a non-local and non-covariant version of the Thirring model in order to describe a many-body system with 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 which allows us to obtain an effective action for the collective excitations of the system. By introducing a non-local version of the self-consistent harmonic approximation, we get an expression for the gap of the charge-density excitations as functional of arbitrary electron–electron potentials. As an example we also consider the case of a non-contact umklapp interaction.