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

TL;DR

This paper argues that quantum field theory on Moyal-Weyl noncommutative spaces can be made equivalent to standard QFT by enforcing twisted Poincare' covariance, making coordinate differences behave undeformed and preserving physical predictions.

Contribution

It demonstrates that with proper covariance enforcement, QFT on Moyal-Weyl spaces aligns with ordinary QFT, addressing previous differences in coordinate behavior.

Findings

Coordinate differences behave undeformed under twisted covariance.

QFT on Moyal-Weyl spaces is compatible with Wightman axioms.

Physical observables are unaffected by noncommutativity.

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.