Numerical analysis of the self-energy in covariant Loop Quantum Gravity

TL;DR

This paper numerically investigates the self-energy radiative corrections in covariant loop quantum gravity, analyzing divergence scaling, the influence of the Barbero-Immirzi parameter, and boundary data effects using advanced numerical methods.

Contribution

It introduces a numerical analysis of the self-energy in covariant loop quantum gravity with new methods and explores divergence behavior and parameter effects.

Findings

Divergence scales approximately linearly with the infrared cutoff.

The Barbero-Immirzi parameter influences the asymptotic behavior.

Boundary data affect the scaling of the self-energy.

Abstract

We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi parameter in the asymptotic behavior, the dependence of the scaling on some boundary data and the expectation values of boundary operators.