Loop-deformed Poincar\'e algebra

TL;DR

This paper provides evidence that loop quantum gravity causes a deformation of the Poincaré algebra at high energies, implying a change in space-time signature and connecting to curved momentum space and relative locality.

Contribution

It introduces a specific realization of the loop-deformed Poincaré algebra and links it to curved momentum space, offering a new perspective on quantum gravity effects.

Findings

Deformation of Poincaré algebra at high energies

Space-time signature changes from Lorentzian to Euclidean

Connection to curved momentum space and relative locality

Abstract

In this essay we present evidence suggesting that loop quantum gravity leads to deformation of the local Poincar\'e algebra within the limit of high energies. This deformation is a consequence of quantum modification of effective off-shell hypersurface deformation algebra. Surprisingly, the form of deformation suggests that the signature of space-time changes from Lorentzian to Euclidean at large curvatures. We construct particular realization of the loop-deformed Poincar\'e algebra and find that it can be related to curved momentum space, which indicates the relationship with recently introduced notion of relative locality. The presented findings open a new way of testing loop quantum gravity effects.