Mutually local fields from form factors

TL;DR

This paper compares two methods for computing form factors in integrable models, demonstrating their equivalence, analyzing their properties, and introducing a generalized class of models with new Lagrangians and scattering matrices.

Contribution

It introduces a new class of Lie algebraic Lagrangians generalizing the Federbush model and evaluates their scattering matrices from first principles.

Findings

Matrix elements satisfy form factor consistency equations with anyonic factors when local.

The Federbush model can be derived from the $SU(3)_3$-homogeneous sine-Gordon model.

Proposed models have explicitly computed scattering matrices.

Abstract

We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in terms of fermionic Fock operators. We compute the corresponding matrix elements for the complex free fermion and the Federbush model. The matrix elements only satisfy the form factor consistency equations involving anyonic factors of local commutativity when the corresponding operators are local. We carry out the ultraviolet limit, analyze the momentum space cluster properties and demonstrate how the Federbush model can be obtained from the $SU(3)_3$-homogeneous sine-Gordon model. We propose a new class of Lagrangians which constitute a generalization of the Federbush model in a Lie algebraic fashion. For these models we evaluate the associated scattering matrices from first principles, which can alternatively also be obtained in a certain limit of the homogeneous sine-Gordon models.