New concept of relativistic invariance in NC space-time: twisted Poincar\'e symmetry and its implications

TL;DR

This paper develops a framework for noncommutative quantum field theory using twisted Poincaré symmetry to ensure relativistic invariance, enabling classification of particles and proving an NC version of Haag's theorem.

Contribution

It introduces a systematic approach to NC QFT based on twisted Poincaré symmetry, extending relativistic invariance concepts to noncommutative space-time.

Findings

Formulation of NC QFT with twisted Poincaré symmetry

Classification of particles via twisted symmetry representations

Proof of NC Haag's theorem

Abstract

We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincar\'e symmetry (with all 10 generators), as proposed in ref. [7]. This allows 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 Poincar\'e 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.