Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

Sabina Alazzawi; Gandalf Lechner

doi:10.1007/s00220-017-2891-0

Communications in Mathematical Physics

September 2017, Volume 354, Issue 3, pp 913–956

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

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Authors and affiliations

Sabina AlazzawiEmail author
Gandalf Lechner

Article

First Online:: 21 June 2017

Received:: 14 September 2016
Accepted:: 27 February 2017

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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

Sabina Alazzawi
- 1
Email authorView author's OrcID profile
Gandalf Lechner
- 2
View author's OrcID profile

1.Zentrum MathematikTechnische Universität MünchenGarchingGermany
2.School of MathematicsCardiff UniversityCardiffUK

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Cite this article as:: Alazzawi, S. & Lechner, G. Commun. Math. Phys. (2017) 354: 913. https://doi.org/10.1007/s00220-017-2891-0

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

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