Violation ofS-matrix factorization in the massive Thirring model

Abstract

We present a counterexample 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. ͓S0556-2821͑98͒06122-0͔

Strong Coupling Limit of Bethe Ansatz Solutions in Massive Thirring Model

“…This is consistent with the recent proof [13] that the S-matrix factorization assumed by Zamolodchikov and Zamolodchikov [14] is violated at the quantum level, and, therefore, the spectrum predicted by the S-matrix factorization is only semiclassical.…”

XXZspin chain in a transverse field as a regularization of the sine-Gordon model

“…Our results are in agreement with DHN formula contrary to previously mentioned papers. We stress that methods used in this paper are independent of previous approaches to SGM (which were criticized in [10][11][12]). We also analyse conformal limit and find conformal dimensions of various states.…”

“…The same method was previously applied to conformal unitary models perturbed by some relevant (usually termal) operator [17][18][19]. In this way we can obtain estimates of mass ratios without further assumptions, particularly those criticized in [10][11][12].…”

“…However, recently appeared claims [10][11][12] that mass spectrum of the MTM is different than (1.1) and that there is only one breather in the whole interval g 0 > 0 (for negative values of g 0 fermion and antifermion repel each other and there are no bound states, like in (1.1)). In [10], using the infinite momentum frame technique and working only in q q sector of the Fock space (neglecting qq q q and higher fermion components), authors obtained the mass of the (only) breather:…”

Properties of the massive Thirring model from theXYZspin chain

“…The additional interest in avoiding the previously mentioned assumptions is due to recent criticism [10][11][12] [the authors claim that there is only one breather in the whole attractive region, and with different mass than the Dashen-Hasslacher-Neveu (DHN) formula predicts]. The same authors challange also the well-known duality relation between the MTM and SGM [13][14][15][16][17].…”