Coherent State Operators in Loop Quantum Gravity

TL;DR

This paper introduces a new method for constructing quantum operators in loop quantum gravity using coherent state quantization, enabling a unified approach to fundamental geometric operators.

Contribution

It develops a coherent state-based framework for defining operators in loop quantum gravity, connecting classical functions to quantum operators via heat kernel coherent states.

Findings

Canonical operators are recovered in the large spin limit.

Constructed operators include holonomy, flux, area, angle, and volume.

The method provides a consistent way to quantize classical functions.

Abstract

We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated to a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins.