U(N) Coherent States for Loop Quantum Gravity

TL;DR

This paper introduces a new set of U(N)-covariant coherent states for SU(2) intertwiners in loop quantum gravity, providing a geometric interpretation related to framed polyhedra and expanding the mathematical tools for quantum geometry.

Contribution

It proposes a novel set of holomorphic operators and coherent states with U(N) covariance, linking algebraic structures to geometric interpretations in quantum gravity.

Findings

States labeled by Grassmannian Gr(N,2) elements

States have a geometric interpretation as framed polyhedra

Related to existing coherent intertwiners

Abstract

We investigate the geometry of the space of N-valent SU(2)-intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners.