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Characterization of Local Observables in Integrable Quantum Field Theories

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Abstract

Integrable quantum field theories in 1+1 dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. Our goal is to characterize these local observables in terms of their expansion coefficients in a series expansion by interacting annihilators and creators, similar to form factors. We establish a rigorous one-to-one characterization, where locality of an observable is reflected in analyticity properties of its expansion coefficients; this includes detailed information about the high-energy behaviour of the observable and the growth properties of the analytic functions. Our results hold for generic observables, not only smeared pointlike fields, and the characterizing conditions depend only on the localization region—we consider wedges and double cones—and on the permissible high energy behaviour.

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Authors and Affiliations

  1. Department of Mathematics, University of York, York, YO10 5DD, UK

    Henning Bostelmann

  2. School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK

    Daniela Cadamuro

Authors
  1. Henning Bostelmann
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  2. Daniela Cadamuro
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Correspondence to Henning Bostelmann.

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Communicated by Y. Kawahigashi

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Bostelmann, H., Cadamuro, D. Characterization of Local Observables in Integrable Quantum Field Theories. Commun. Math. Phys. 337, 1199–1240 (2015). https://doi.org/10.1007/s00220-015-2294-z

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