U(N) tools for Loop Quantum Gravity: The Return of the Spinor

Understand

We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints.

• We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals.
• We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space.
• In particular, we translate the usual loop gravity holonomy observables to our classical framework.