Characterization of local observables in integrable quantum field theories

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.

minor changes, as to appear in Commun. Math. Phys.; 39 pages, 4 figures, 1 video

References in corpus (4)

• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• Characterization of local observables in integrable quantum field theories
• Quantum Inequalities from Operator Product Expansions
• An operator expansion for integrable quantum field theories

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• Wedge-local fields in integrable models with bound states
• Quantum energy inequalities in integrable models with several particle species and bound states
• Towards an explicit construction of local observables in integrable quantum field theories
• Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level
• Direct construction of pointlike observables in the Ising model
• Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor
• On the status of pointlike fields in integrable QFTs