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Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

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Abstract

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang–Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O(N)-invariant nonlinear \({\sigma}\)-models.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Sabina Alazzawi

  2. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK

    Gandalf Lechner

Authors
  1. Sabina Alazzawi
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  2. Gandalf Lechner
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Correspondence to Sabina Alazzawi.

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Communicated by Y. Kawahigashi

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Alazzawi, S., Lechner, G. Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories. Commun. Math. Phys. 354, 913–956 (2017). https://doi.org/10.1007/s00220-017-2891-0

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