Coherent states for quantum gravity: towards collective variables

TL;DR

This paper develops a framework for constructing coherent states in loop quantum gravity that focus on collective geometric observables, addressing key subtleties related to diffeomorphism invariance and continuum approximation.

Contribution

It introduces a revised approach to defining coherent states for collective variables, enhancing the approximation of continuum geometry in quantum gravity models.

Findings

Coherent states for collective observables can better approximate continuum geometry.

Addressed subtleties related to diffeomorphism invariance in state construction.

Provided a concrete example relevant for quantum cosmology applications.

Abstract

We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the diffeomorphism invariance of the theory. Aiming at approximating a continuum geometry in terms of discrete, graph-based data, we focus on coherent states for collective observables characterizing both the intrinsic and extrinsic geometry of the hypersurface, and we argue that one needs to revise accordingly the more local definitions of coherent states considered in the literature so far. In order to clarify the concepts introduced, we work through a concrete example that we hope will be useful to applying coherent state techniques to cosmology.