On bosonic Thirring model in Minkowski signature

Abstract

We present the way to continue the bosonic Thirring model or βγ-system with quartic interaction to Minkowski signature, based on the symmetries of this model. It is shown that the considered Minkowski version of the model is one-loop renormalizable. Based on this, we find the amplitudes of scattering of the excitations corresponding to the γ and γ¯ fields up to the one-loop order. In particular, it was computed that the 2→2 amplitudes of these excitations possess property of reflectionless scattering and thus the corresponding S-matrix of such excitations satisfies the Yang-Baxter equation. The obtained S-matrix elements for γ and γ¯ are shown to coincide with the corresponding S-matrix elements of the solitons in the complex sine-Gordon model proposed by Dorey and Hollowood.