Violation of S-matrix factorization in massive Thirring model

TL;DR

This paper demonstrates that the S-matrix factorization property does not hold in the massive Thirring model, challenging assumptions about its quantum integrability and the relationship to the sine-Gordon model.

Contribution

It provides a numerical counterexample showing the violation of S-matrix factorization in the massive Thirring model, highlighting the non-commutativity of crossing symmetry and factorization.

Findings

S-matrix factorization is violated in the massive Thirring model.

Crossing symmetry and factorization do not commute in this model.

The soliton S-matrix picture is semiclassical and incomplete for quantization.

Abstract

We present a counter example which shows the violation of the S-matrix factorization in the massive Thirring model. This is done by solving the PBC equations of the massive Thirring model exactly but numerically. The violation of the S-matrix factorization is related to the fact that the crossing symmetry and the factorization do not commute with each other. This confirms that the soliton antisoliton S-matrix factorization picture of the sine-Gordon model is semiclassical and does not lead to a full quantization procedure of the massive Thirring model.