Asymptotic of Lorentzian Polyhedra Propagator

Understand

A certain operator $\T=\int_{\SL}\dd g\, Y^{\dagger}gY$ can be found in various Lorentzian EPRL calculations.

• The properties of this operator has been studied here in large $j$ limit.
• The leading order of $\T$ is proportional to the identity operator.
• Knowing the operator $\T$ one can renormalize spin-foam's edge self-energy by computing the amplitude of sum of a series of edges with increasing number of vertices and bubbles.