Wedge-local fields in interacting quantum field theories with bound states

TL;DR

This paper discusses the construction of wedge-local fields in interacting quantum field theories with bound states, extending previous models to include richer particle spectra such as Z(N)-Ising and affine-Toda theories.

Contribution

It introduces a new construction of wedge-local fields incorporating bound states via a deformation of existing models, advancing the operator-algebraic approach to QFT.

Findings

Extended Lechner's models to include bound states

Constructed wedge-local fields with a bound state operator

Identified open problems in the construction process

Abstract

In the context of constructing interacting quantum field theories in the operator-algebraic approach, wedge-local fields play an important role. After the work of Lechner to construct factorizing scattering matrix models with scalar S-matrices without bound states, we recently extended this construction to a class of models with a richer particle spectrum and which are believed to have bound states. These include the Z(N)-Ising model and the affine-Toda field theories. This construction is done by exhibiting wedge-local fields which arise as a deformation of Lechner's fields with the so called "bound state operator". I will review the main passages of this construction and explain the open problems.