Non local Thirring model with backward and umklapp interactions

Details Non local Thirring model with backward and umklapp interactions Non local Thirring model with backward and umklapp interactions

2001-12-07

arxiv.org/abs/hep-th/0112057v1

Nucl.Phys. B636 (2002) 514-528

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, no figures

Scientific paper

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.

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