Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories

Lechner G, Schuetzenhofer C (2014)

Publication Type: Journal article

Publication year: 2014


Book Volume: 15

Pages Range: 645-678

Journal Issue: 4

DOI: 10.1007/s00023-013-0260-x


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. © 2013 Springer Basel.

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Lechner, G., & Schuetzenhofer, C. (2014). Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories. Annales Henri Poincaré, 15(4), 645-678.


Lechner, Gandalf, and Christian Schuetzenhofer. "Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories." Annales Henri Poincaré 15.4 (2014): 645-678.

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