CastroAlvaredo, O. & Fring, A. (2005). Integrable models with unstable particles. Progress in Mathematics, 237, pp. 5987. doi: 10.1007/3764373415_2

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Abstract
We review some recent results concerning integrable quantum field theories in 1+1 spacetime 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 solitonantisoliton sector of the elliptic sineGordon model in terms of infinite products of qdeformed 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 Smatrix 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.
Item Type:  Article 

Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/702 
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