Note on four-particle form factors of operators $T_{2n}T_{-2n}$ in sinh-Gordon model

TL;DR

This paper analytically computes four-particle form factors of specific operators in the sinh-Gordon model, confirming previous proposals and demonstrating the effectiveness of the algebraic approach in quantum integrable models.

Contribution

It provides explicit formulas for four-particle form factors of $T_{2n}T_{-2n}$ operators, validating earlier theoretical predictions in the sinh-Gordon model.

Findings

Confirmed the proposal by Smirnov and Zamolodchikov for these matrix elements

Demonstrated the effectiveness of the algebraic approach to form factors

Provided explicit analytical expressions for the form factors

Abstract

The diagonal matrix elements $\langle\theta_1,\theta_2|T_{2n}T_{-2n}|\theta_1,\theta_2\rangle$ between two-particle states in the sinh-Gordon model are computed analytically for all integers $n>0$. This confirms the proposal by F. Smirnov and A. Zamolodchikov for these matrix elements and demonstrates effectiveness of the algebraic approach to form factors.