On Locality in Quantum General Relativity and Quantum Gravity

TL;DR

This paper explores the concept of locality in quantum general relativity, proposing a quantum-geometric framework that incorporates a fundamental length and aligns with key principles like the equivalence principle and path integrals.

Contribution

It introduces a novel formulation of quantum-geometric locality based on local quantum frames and extends it to quantum spacetime, advancing understanding of quantum gravity's geometric structure.

Findings

Quantum-geometric locality incorporates a fundamental length.

The formulation aligns with the strong equivalence principle.

Extension to quantum spacetime provides a new perspective on quantum gravity.

Abstract

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.