Form factors from free fermionic Fock fields, the Federbush model

TL;DR

This paper develops a fermionic Fock space representation of the Federbush model, analyzing its form factors, locality conditions, and connections to sine-Gordon models, providing new insights into its algebraic structure.

Contribution

It introduces a fermionic Fock space framework for the Federbush model and links it to sine-Gordon models through a generalized Lagrangian.

Findings

Matrix elements satisfy form factor consistency equations

Federbush model derived from $SU(3)_3$-homogeneous sine-Gordon model

Proposed a generalized Lie algebraic Lagrangian

Abstract

By representing the field content as well as the particle creation operators in terms of fermionic Fock operators, we compute the corresponding matrix elements of the Federbush model. Only when these matrix elements satisfy the form factor consistency equations involving anyonic factors of local commutativity, 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 Lagrangian which on one hand constitutes a generalization of the Federbush model in a Lie algebraic fashion and on the other a certain limit of the homogeneous sine-Gordon models.