We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e., diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, Möbius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the 2-dimensional Minkowski space, which—although being diffeomorphism covariant—does not have the split property.

Conformal Covariance and the Split Property / Morinelli, V.; Tanimoto, Y.; Weiner, M.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 357:1(2018), pp. 379-406. [10.1007/s00220-017-2961-3]

Conformal Covariance and the Split Property

Morinelli V.;
2018

Abstract

We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e., diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, Möbius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the 2-dimensional Minkowski space, which—although being diffeomorphism covariant—does not have the split property.
2018
Algebraic Quantum Field Theory, Operator Algebras, Conformal symmetry
01 Pubblicazione su rivista::01a Articolo in rivista
Conformal Covariance and the Split Property / Morinelli, V.; Tanimoto, Y.; Weiner, M.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 357:1(2018), pp. 379-406. [10.1007/s00220-017-2961-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1584707
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