# Wedge-Local Quantum Fields and Noncommutative Minkowski Space

June 27, 2007

Within the setting of a recently proposed model of quantum fields on
noncommutative Minkowski spacetime, the consequences of the consistent
application of the proper, untwisted Poincare 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 of 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.

Keywords:

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