The diffeomorphism algebra approach to quantum gravity

TL;DR

This paper explores the representation theory of extended Lie algebras related to spacetime symmetries, offering new insights into quantum gravity and addressing longstanding issues like diffeomorphism roles and causal structure.

Contribution

It introduces a novel approach using non-centrally extended Lie algebras to better understand quantum gravity and spacetime symmetries.

Findings

Addresses the role of diffeomorphisms in quantum gravity

Provides a framework for representing spacetime symmetries

Solves longstanding problems related to causal structure

Abstract

The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer's trajectory, has recently been developped. It naturally solves some long-standing problems in quantum gravity, e.g. the role of diffeomorphisms and the causal structure, but some new questions also arise.