Amplitude zeroes in collinear processes or what is left from a factorizable 2D model in higher dimensions

We show that for collinear processes, i.e. processes where the incoming and outgoing momenta are aligned along the same line, the S matrix of the tree level 2 + 1 dimensional Thirring model factorizes: any S-matrix element is a product of 2 → 2 elements. In particular this means nullification of all collinear 2 → n amplitudes for n > 2.