Background-free propagation in loop quantum gravity
Simone Speziale
TL;DR
This paper surveys a general boundary framework for defining n-point functions in loop quantum gravity via spin foam amplitudes and group field theory. It develops a double perturbative scheme in the Planck length $\ell_{ m P}$ and in the spin foam coupling $\lambda$, analyzes gauge fixing and renormalization in 3D and 4D models, and examines the semiclassical limit through boundary states peaked on classical geometries. It demonstrates that the Barrett–Crane 4D model fails to reproduce GR's semiclassical behavior, motivating the EPRL/FK family with coherent boundary states and angle variables to recover metric-like dynamics, supported by preliminary analytical and numerical evidence. The discussion highlights the central role of a dynamical semiclassical boundary state and the challenges of summing over triangulations to achieve a consistent continuum limit, offering a falsifiable path toward connecting loop quantum gravity with low-energy general relativity.
Abstract
I review the definition of n-point functions in loop quantum gravity, discussing what has been done and what are the main open issues. Particular attention is dedicated to gauge aspects and renormalization.