The projector on physical states in loop quantum gravity

TL;DR

This paper introduces a new projector operator for physical states in loop quantum gravity, establishing a covariant spacetime formalism that connects to spin foam models and enables computation of physical expectation values.

Contribution

It constructs a diffeomorphism-invariant projector operator in loop quantum gravity, linking it to spin foam models and providing a framework for calculating physical quantities.

Findings

Defined a covariant projector operator for physical states

Connected the formalism to spin foam models

Outlined a method for computing expectation values

Abstract

We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like, spacetime formalism for quantum gravity and relates this theory to the spin foam models. We also discuss how expectation values of physical quantity can be computed.