Group field theory as the 2nd quantization of Loop Quantum Gravity

TL;DR

This paper reformulates canonical Loop Quantum Gravity into a second quantized framework using a Fock space of spin networks, establishing a direct link to Group Field Theory and spin foam models, exemplified in 3D quantum gravity.

Contribution

It introduces a second quantized reformulation of LQG as a Fock space of spin networks, connecting canonical dynamics to GFT and spin foam models.

Findings

Establishes a general correspondence between LQG and GFT dynamics.

Derives a specific GFT model from canonical LQG.

Demonstrates the approach with 3D quantum gravity example.

Abstract

We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.