Can QFT on Moyal-Weyl spaces look as on commutative ones?

Abstract

We sketch a natural affirmative answer to the question based on a joint work [11] with J. Wess. There we argue that a proper enforcement of the "twisted Poincare'" covariance makes any differences $(x-y{)}^{\mu }$ of coordinates of two copies of the Moyal-Weyl deformation of Minkowski space like undeformed. Then QFT in an operator approach becomes compatible with (minimally adapted) Wightman axioms and time-ordered perturbation theory, and physically equivalent to ordinary QFT, as observables involve only coordinate differences.

Talk given at the 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics "Noncommutative Geometry and Spacetime in Physics", Nishinomiya-Kyoto, Nov. 2006

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