Integrable Models with Unstable Particles

  • Olalla Castro-Alvaredo
  • Andreas Fring
Part of the Progress in Mathematics book series (PM, volume 237)

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.

Keywords

Exactly and quasi-solvable systems S-matrix theory model quantum field theories two-dimensional field theories conformal field theories infinite-dimensional groups and algebras motivated by physics including Virasoro Kac-Moody 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Olalla Castro-Alvaredo
    • 1
  • Andreas Fring
    • 2
  1. 1.Laboratoire de Physique, Ecole Normale Supérieure de LyonUMR 5672 du CNRSLyon CEDEXFrance
  2. 2.Centre for Mathematical SciencesCity UniversityLondonUK

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