The continuum limit of loop quantum gravity - a framework for solving the theory

TL;DR

This paper discusses constructing a continuum limit in loop quantum gravity by developing iterative coarse graining methods to obtain the physical Hilbert space, aiming to complete the theory.

Contribution

It introduces a framework for deriving the continuum physical Hilbert space using coarse graining and renormalization flow techniques in loop quantum gravity.

Findings

Coarse graining methods can construct physical states in a truncation scheme.

The scheme acts as a renormalization flow for the theory.

Diffeomorphism symmetry indicates the approach to the continuum limit.

Abstract

The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the solutions of the theory. We present iterative coarse graining methods to construct physical states in a truncation scheme and explain in which sense this scheme represents a renormalization flow. We comment on the role of diffeomorphism symmetry as an indicator for the continuum limit.