Self-energy and vertex radiative corrections in LQG

TL;DR

This work analyzes radiative-correction diagrams in loop quantum gravity using the spinfoam formalism, focusing on two elementary bubbles that correspond to one-loop self-energy and vertex corrections. It derives the naive infrared divergence degrees of these diagrams under different normalizations for face amplitudes and fusion coefficients, showing that convergence is highly sensitive to these choices. In particular, a natural tilde-fusion normalization yields finiteness for both diagrams across a broad range of the exponent k, while other normalizations can produce power or logarithmic divergences. The findings highlight how discretization and normalization choices regulate divergences in LQG and motivate further study of regularization across the full set of diagrams and their physical implications.

Abstract

We consider the elementary radiative-correction terms in loop quantum gravity. These are a two-vertex "elementary bubble" and a five-vertex "ball"; they correspond to the one-loop self-energy and the one-loop vertex correction of ordinary quantum field theory. We compute their naive degree of (infrared) divergence.

Figures (3)

• Figure 1: The self-energy spinfoam. Left: boundary variables. Right: internal variables (only one of the six internal faces is highlighted).
• Figure 2: The self-energy bubble. Left: the six faces. Right: equatorial section.
• Figure 3: The "ball" vertex amplitude. Left: the five vertices and the ten+five edges. Right: one internal face and one external face are shown.