New Concept of Relativistic Invariance in Noncommutative Space-Time: Twisted Poincaré Symmetry and Its Implications

We present a systematic framework for noncommutative (NC) quantum field theory (QFT) within the new concept of relativistic invariance based on the notion of twisted Poincaré symmetry, as proposed by Chaichian et al. [Phys. Lett. B 604, 98 (2004)]. This allows us to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincaré symmetry and as a result for the NC versions of $CPT$ and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag’s theorem.