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

Understand

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.