Algebraic approach to quantum gravity II: noncommutative spacetime

TL;DR

This paper introduces a noncommutative geometric framework for quantum gravity, focusing on bicrossproduct models of spacetime and their physical implications, including variable light speed and Lorentz transformations.

Contribution

It provides a detailed account of bicrossproduct noncommutative spacetimes and explores their global Poincaré group properties, advancing the understanding of quantum gravity models.

Findings

Bicrossproduct models of spacetime are thoroughly analyzed.

Predictions include a variable speed of light in noncommutative spacetime.

Off-shell momentum can be boosted to infinite negative energy via Lorentz transformations.

Abstract

We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t,x_i]=i \lambda x_i and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincar\'e group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton.