A lattice worldsheet sum for 4-d Euclidean general relativity

TL;DR

This paper introduces a lattice model for 4D Euclidean quantum gravity that sums over spin network worldsheets, linking discrete quantum geometry with classical general relativity in a novel, spin-based discretization framework.

Contribution

It proposes a new lattice model for Euclidean quantum gravity using spin network worldsheets, connecting canonical loop quantum gravity with a sum-over-geometries approach.

Findings

Model expresses quantum gravity as a sum over spin network worldsheets.

Spacetime discreteness arises naturally from spin spectrum, not a fixed lattice.

Reproduces classical Euclidean GR in the continuum limit.

Abstract

A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks, and an interpretation of these worldsheets as spacetime geometries is given, based on the geometry defined by spin networks in canonical loop quantized GR. The spacetime geometry has a Planck scale discreteness which arises "naturally" from the discrete spectrum of spins of SU(2) representations (and not from the use of a spacetime lattice). The lattice model of the dynamics is a formal quantization of the classical lattice model of \cite{Rei97a}, which reproduces, in a continuum limit, Euclidean general relativity.