On bosonic Thirring model in Minkowski signature

We present the way to continue the bosonic Thirring model or betagamma-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 the scattering of the excitations corresponding to the gamma and gammatilde fields up to the one loop order. In particular, it was computed that the 2->2 amplitudes of these excitations possess the property of reflectionless scattering and thus the corresponding S-matrix of such excitations satisfies the Yang-Baxter equation. The obtained S-matrix elements for gamma and gammatilde are shown to coincide with the corresponding S-matrix elements of the solitons in the complex sine-Gordon model proposed by Dorey and Hollowood.