# Noncommutative Deformations of Wightman Quantum Field Theories

August 26, 2008

Quantum field theories on noncommutative Minkowski space are studied in a
model-independent setting by treating the noncommutativity as a deformation of
quantum field theories on commutative space. Starting from an arbitrary
Wightman theory, we consider special vacuum representations of its Weyl-Wigner
deformed counterpart. In such representations, the effect of the
noncommutativity on the basic structures of Wightman theory, in particular the
covariance, locality and regularity properties of the fields, the structure of
the Wightman functions, and the commutative limit, is analyzed. Despite the
nonlocal structure introduced by the noncommutativity, the deformed quantum
fields can still be localized in certain wedge-shaped regions, and may
therefore be used to compute noncommutative corrections to two-particle
S-matrix elements.

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