# Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox

## TL;DR

This paper discusses the development of a computational toolbox for studying quantum gravity within the Asymptotic Safety framework, focusing on non-perturbative effects on matter propagation and spacetime structure.

## Contribution

It introduces a set of technical methods for analyzing non-perturbative quantum corrections in gravity-matter systems within Asymptotic Safety.

## Key findings

- Computed momentum-dependent two-point function for scalar fields influenced by quantum geometry
- Demonstrated the toolbox's capability to analyze quantum spacetime effects
- Provided insights into matter propagation on fluctuating quantum spacetimes

## Abstract

Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and gravity-matter systems in the non-perturbative regime has put many interesting physical questions within reach. In particular, the construction of the non-perturbative quantum corrections to the propagation of fields on a fluctuating spacetime allows addressing the effective propagation of matter on a quantum spacetime or the possible resolution of spacetime singularities based on first principle computations. In this article, we assemble a technical toolbox for carrying out investigations on this promising research frontier. As a specific example we present results for the momentum-dependent two-point function for a scalar field induced by the quantum fluctuations of the underlying geometry in a self-consistent way.