O(1/N_f) Corrections to the Thirring Model in 2<d<4
Abstract
The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.
Keywords
Cite
@article{arxiv.hep-th/9411016,
title = {O(1/N_f) Corrections to the Thirring Model in 2<d<4},
author = {Simon Hands},
journal= {arXiv preprint arXiv:hep-th/9411016},
year = {2009}
}
Comments
22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected)