Gravitation in terms of observables

TL;DR

This paper proposes a novel loop-based formalism for gravity that emphasizes observables and aims to provide a new quantum representation, distinct from existing approaches like loop quantum gravity.

Contribution

It extends the loop and open path formalism to gravity, offering a gauge-invariant, constraint-free quantum framework based on Dirac observables.

Findings

Formalism describes spacetime geometry via gauge-invariant functions.

Potential for a constraint-free reduced phase space quantization.

Provides a new perspective on quantum gravity beyond current models.

Abstract

In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a complete set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.