Integrable models with unstable particles

TL;DR

This paper reviews integrable quantum field theories in 1+1 dimensions with unstable particles, introduces a bootstrap principle for their spectra, and explores their algebraic structures, scattering amplitudes, and reductions to new models.

Contribution

It proposes a new bootstrap approach for constructing spectra with unstable particles and describes the underlying Lie algebraic structure and decoupling rule.

Findings

Developed a bootstrap principle for unstable particles

Derived scattering amplitudes for elliptic sine-Gordon model

Constructed an elliptic SO(n)-affine Toda field theory

Abstract

We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to integrable models, we subsequently propose a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We describe the general Lie algebraic structure which underlies theories with unstable particles and formulate a decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. We extend these ideas to theories with an infinite spectrum of unstable particles. We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-Gordon model in terms of infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. For that situation we compute the complete S-matrix of all sectors. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal SO(n)-affine Toda field theory.