Numerical analysis of the self-energy in covariant loop quantum gravity

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.