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Infinite Dimensional Algebras and Quantum Integrable Systems pp 59–87Cite as

Integrable Models with Unstable Particles

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Part of the book series: Progress in Mathematics ((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.

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Author information

Authors and Affiliations

  1. Laboratoire de Physique, Ecole Normale Supérieure de Lyon, UMR 5672 du CNRS, 46 Allée d’Italie, F-69364, Lyon CEDEX, France

    Olalla Castro-Alvaredo

  2. Centre for Mathematical Sciences, City University, Northampton Square, London, EC1V 0HB, UK

    Andreas Fring

Authors
  1. Olalla Castro-Alvaredo
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  2. Andreas Fring
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Editor information

Editors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontaka 27, 191011, St. Petersburg, Russia

    Petr P. Kulish

  2. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Nenad Manojlovich

  3. IInd Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

    Henning Samtleben

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Castro-Alvaredo, O., Fring, A. (2005). Integrable Models with Unstable Particles. In: Kulish, P.P., Manojlovich, N., Samtleben, H. (eds) Infinite Dimensional Algebras and Quantum Integrable Systems. Progress in Mathematics, vol 237. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7341-5_2

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