Coherent States and Particle Scattering in Loop Quantum Gravity

TL;DR

This paper explores a novel connection between particle scattering in Loop Quantum Gravity and the positive Grassmannian, aiming to bridge LQG with flat space quantum field theory.

Contribution

It establishes a correspondence between scattering kinematic data and U(N) coherent states in LQG, proposing a new framework for quantum gravity dynamics.

Findings

Identifies a link between LQG states and the positive Grassmannian.

Provides a foundation for a scattering theory within LQG.

Suggests a pathway to connect LQG with flat space QFT.

Abstract

Quantum field theory provides us with the means to calculate scattering amplitudes. In recent years a dramatic new development has lead to great simplification of such calculations. This is based on the discovery of the``amplituhedron'' in the context of scattering of massless gauge bosons in Yang-Mills theory. One of the main challenges facing Loop Quantum Gravity is the lack of a clear description of particle scattering processes and a connection to flat space QFT. Here we show a correspondence between the space of kinematic data of the scattering $ N $ massless particles and $ U(N) $ coherent states in LQG. This correspondence allows us to provide the outlines of a theory of quantum gravity based upon the dynamics of excitations living on the the positive Grassmannian.