New tools for Loop Quantum Gravity with applications to a simple model

TL;DR

This paper reviews recent developments in Loop Quantum Gravity, introducing new tools like the U(N) framework and spinor representation, and applies them to a simplified model to propose a dynamics and explore cosmological analogies.

Contribution

It introduces the U(N) framework and spinor representation as new tools for Loop Quantum Gravity and applies them to a simplified model to develop a dynamics.

Findings

Proposes a new dynamics for a symmetry reduced sector of Loop Quantum Gravity.

Establishes a classical setting for the U(N) framework using spinors.

Draws analogies between the simplified model and Loop Quantum Cosmology.

Abstract

Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field at large scales. Here we will review the recent U(N) framework for Loop Quantum Gravity and the new spinor representation (that provides a classical setting for the U(N) framework). Then, we will apply these techniques to a simple model in order to propose a dynamics for a symmetry reduced sector of the theory. Furthermore, we will explore certain analogies of this model with Loop Quantum Cosmology.