On the Correspondence between Poincar\'e Symmetry of Commutative QFT and Twisted Poincar\'e Symmetry of Noncommutative QFT

TL;DR

This paper establishes a deep correspondence between the twisted Poincaré symmetry in noncommutative quantum field theories and the standard Poincaré symmetry in commutative theories, revealing that their equivalence extends beyond correlation functions to their symmetries.

Contribution

It demonstrates the explicit correspondence between twisted Poincaré symmetry in noncommutative QFT and Poincaré symmetry in commutative QFT, including conserved charges, showing a deeper equivalence.

Findings

The twisted Poincaré symmetry can be related to the standard Poincaré symmetry.

Conserved charges associated with twisted symmetry are constructed.

The equivalence extends to symmetries, not just correlation functions.

Abstract

The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincar\'e algebra, while that of standard commutative quantum field theories is described by the Poincar\'e algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincar\'e symmetry of the deformed theory and the Poincar\'e symmetry of a commutative theory is established. As a by-product, we obtain the conserved charge associated with the twisted Poincar\'e transformation to make the twisted Poincar\'e symmetry evident in the deformed theory. Our result implies that the equivalence between the commutative theory and the deformed theory holds in a deeper level, i.e., it holds not only in correlation functions but also in (different types of) symmetries.