Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model

TL;DR

This paper develops a method to explicitly compute form factors in integrable quantum field theories, exemplified on the sine-Gordon model, using minimal analyticity and the LSZ formalism, and confirms results through perturbation theory.

Contribution

It introduces a novel approach to derive explicit form factors in integrable models based on minimal analyticity and Riemann-Hilbert problems, with solutions for the sine-Gordon model.

Findings

Explicit formulas for form factors in the sine-Gordon model.

Validation of the formalism through perturbation theory comparison.

Solution for form factors with an odd number of particles.

Abstract

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "minimal analyticity" and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. We carry out a consistency check for the solution of the three particle form factor against the Thirring model perturbation theory and thus confirm the general formalism.