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

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

1998-10-07

arxiv.org/abs/hep-th/9810048v1

Theor.Math.Phys.118:385-391,1999; Teor.Mat.Fiz.118:488-496,1999

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex, no figures. Submitted to Teor.Mat.Fiz. (Russia), Proceedings of the Second International Conference on Exactl

Scientific paper

10.1007/BF02557337

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.

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