Annales Henri Poincaré

, Volume 15, Issue 4, pp 645–678 | Cite as

Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories

  • Gandalf Lechner
  • Christian Schützenhofer


The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species transforming under a global gauge group. Starting from a two-particle S-matrix satisfying the usual requirements (unitarity, Yang–Baxter equation, Poincaré and gauge invariance, crossing symmetry, . . .), a pair of relatively wedge-local quantum fields is constructed which determines the field net of the model. Although the verification of the modular nuclearity condition as a criterion for the existence of local fields is not carried out in this paper, arguments are presented that suggest it holds in typical examples such as non-linear O(N)   σ-models. It is also shown that for all models complying with this condition, the presented construction solves the inverse scattering problem by recovering the S-matrix from the model via Haag–Ruelle scattering theory, and a proof of asymptotic completeness is given.


Scalar Case Mass Shell Double Cone Integrable Quantum Inverse Scattering Problem 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of PhysicsVienna UniversityViennaAustria
  2. 2.Institute for Theoretical PhysicsLeipzig UniversityLeipzigGermany

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