Twisted Poincar\'e Invariant Quantum Field Theories

TL;DR

This paper develops quantum field theories on the Moyal plane that are invariant under a twisted Poincaré group action, introducing a systematic approach to ensure symmetry and S-matrix invariance using quantum fields.

Contribution

It introduces a systematic construction of quantum field theories with twisted Poincaré invariance, including the novel development of Poincaré generators from quantum fields.

Findings

Quantum field theories invariant under twisted Poincaré action are formulated.

The S-matrix invariance under the twisted group action is established.

A new method for constructing Poincaré generators from quantum fields is presented.

Abstract

It is by now well known that the Poincar\'e group acts on the Moyal plane with a twisted coproduct. Poincar\'e invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincar\'e action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincar\'e group, ensuring also the invariance of the S-matrix under the twisted action of the group . A significant new contribution here is the construction of the Poincar\'e generators using quantum fields.