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Towards an operator-algebraic construction of integrable global gauge theories

Lechner, Gandalf and Schützenhofer, Christian 2014. Towards an operator-algebraic construction of integrable global gauge theories. Annales Henri Poincare 15 (4) , pp. 645-678. 10.1007/s00023-013-0260-x

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 1424-0637
Date of First Compliant Deposit: 30 March 2016
Last Modified: 19 Oct 2019 02:23
URI: http://orca.cf.ac.uk/id/eprint/73597

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