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Wedge-local quantum fields and noncommutative minkowski space

Grosse, Harald and Lechner, Gandalf 2007. Wedge-local quantum fields and noncommutative minkowski space. Journal of High Energy Physics 2007 (11) , 012. 10.1088/1126-6708/2007/11/012

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Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski space, the consequences of the consistent application of the proper, untwisted Poincaré group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region in Minkowski space. This assignment is consistent with the principles of covariance and locality, i.e. fields localized in spacelike separated wedges commute. Regarding the model as a non-local, but wedge-local, quantum field theory on ordinary (commutative) Minkowski spacetime, it is possible to determine two-particle S-matrix elements, which turn out to be non-trivial. Some partial negative results concerning the existence of observables with sharper localization properties are also obtained.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: IOP Science
ISSN: 1029-8479
Last Modified: 04 Jun 2017 08:09

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