On the Representation of Minimal Form Factors in Integrable Quantum Field Theory

TL;DR

This paper introduces a novel representation of minimal form factors in integrable quantum field theories, specifically for the sinh-Gordon model, by decomposing them into elementary components to facilitate analysis and computation.

Contribution

The authors present a new way to express minimal form factors as a sum of elementary terms, extending the understanding of form factors in integrable models and their relation to $ ext{T}ar{ ext{T}}$ perturbations.

Findings

Explicit decomposition of minimal form factors into elementary building blocks.

Extension of the representation to other integrable quantum field theories.

Potential improvements in numerical evaluation of correlation functions.

Abstract

In this paper, we propose a new representation of the minimal form factors in integrable quantum field theories. These are solutions of the two-particle form factor equations, which have no poles on the physical sheet. Their expression constitutes the starting point for deriving higher particle form factors and, from these, the correlation functions of the theory. As such, minimal form factors are essential elements in the analysis of integrable quantum field theories. The proposed new representation arises from our recent study of form factors in $\mathrm{T}\overline{\mathrm{T}}$-perturbed theories, where we showed that the minimal form factors decompose into elementary building blocks. Here, focusing on the paradigmatic sinh-Gordon model, we explicitly express the standard integral representation of the minimal form factor as a combination of infinitely many elementary terms, each representing the minimal form factor of a generalised $\mathrm{T}\overline{\mathrm{T}}$ perturbation of the free fermion. Our results can be readily extended to other integrable quantum field theories and open various relevant questions and discussions, from the efficiency of numerical methods in evaluating correlation functions to the foundational question of what constitutes a "reasonable" choice for the minimal form factor.