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Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories

Autor(en)

Gandalf Lechner, Christian Schützenhofer

Abstrakt

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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Wien

Journal

Annales Henri Poincare

Band

Seiten

645-678

Anzahl der Seiten

ISSN

1424-0637

DOI

https://doi.org/10.1007/s00023-013-0260-x

Publikationsdatum

04-2014

Peer-reviewed

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Nuclear and High Energy Physics, Statistical and Nonlinear Physics, Mathematical Physics

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