  We present the way to continue the bosonic Thirring model or
$\beta\gamma$-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
$\bar{\gamma}$ fields up to the one-loop order. In particular, it was computed
that the $2 \rightarrow 2$ 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 $\bar{\gamma}$ are shown to coincide with the
corresponding $S$-matrix elements of the solitons in the complex sine-Gordon
model proposed by Dorey and Hollowood.
