# Towards Gaussian states for loop quantum gravity

## TL;DR

This paper explores the construction of Gaussian-like semiclassical states in loop quantum gravity, reformulating the algebraic structure to develop states that better approximate classical geometry across all degrees of freedom.

## Contribution

It introduces a reformulation of the U(1) holonomy-flux algebra as a Weyl algebra and proposes a new class of quasifree-like states for all degrees of freedom in LQG.

## Key findings

- Reformulation of the algebra as a Weyl algebra
- Development of a new class of Gaussian-like states
- Potential for improved semiclassical approximations in LQG

## Abstract

An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. To obtain a toy-model we reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra, and discuss generalisations to SU(2). We then define and investigate a new class of states on these algebras which behave like quasifree states on the momentum variables.