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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
Article

Abstract

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.

Keywords

Scalar Case Mass Shell Double Cone Integrable Quantum Inverse Scattering Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

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

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