Review of Twisted Poincare Symmetry

TL;DR

This review discusses the mathematical construction and physical applications of twisted Poincare symmetry in quantum field theories on noncommutative spaces, highlighting its implications for quantum gravity and cosmology.

Contribution

It provides a comprehensive overview of twisted Poincare-covariant quantum fields, their mathematical foundation via Drinfeld twists, and explores their applications in quantum gravity and cosmological models.

Findings

Twisted Poincare symmetry can be applied to quantum fields on the Moyal plane.

Constraints on spacetime noncommutativity can be derived from CMB anisotropy data.

Differences between Moyal and Voros quantum fields are significant for their applications.

Abstract

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on the Moyal plane. The Drinfeld twist, which plays a key mathematical role in this construction, is then applied to the case of discrete groups, with a view to applications to geons in quantum gravity. The Poincare-twisted fields can also be applied to study the CMB anisotropies, and corrections to the power spectrum are used to put constraints on spacetime noncommutativity. The article also addresses the issue of the difference between Moyal and Voros quantum fields. Finally, it is pointed out that the Euclidean functional integrals of QFTs on the Moyal plane do not, in general, obey reflection positivity.