Path-integral formulation of backward and umklapp scattering for 1d spinless fermions
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9810048,
title = {Path-integral formulation of backward and umklapp scattering for 1d spinless fermions},
author = {V. I. Fernández and C. M. Naón},
journal= {arXiv preprint arXiv:hep-th/9810048},
year = {2011}
}
Comments
12 pages, latex, no figures. Submitted to Teor.Mat.Fiz. (Russia), Proceedings of the Second International Conference on Exactly Solvable in Mathematical Physics, Chelyabinsk, Russia, August 1998. Authors names corrected