On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces

Understand

We explore some general consequences of a consistent formulation of relativistic quantum field theory (QFT) on the Groenewold-Moyal-Weyl noncommutative versions of Minkowski space with covariance under the twisted Poincare' group of Chaichian et al.

• [12], Wess [44], Koch et al.
• [31], Oeckl [34].
• We argue that a proper enforcement of the latter requires braided commutation relations between any pair of coordinates $\hat x,\hat y$ generating two different copies of the space, or equivalently a $\star$-tensor product $f(x)\star g(y)$ (in the parlance of Aschieri et al.