Simple Spin Networks as Feynman Graphs

TL;DR

This paper introduces a novel approach to evaluating simple spin networks as Feynman integrals, enabling analysis of higher-dimensional quantum gravity models and deriving their asymptotic behavior related to the Regge action.

Contribution

It presents a new formalism for describing and evaluating simple SO(D) spin networks as Feynman integrals, facilitating higher-dimensional quantum gravity research.

Findings

Derived the asymptotics of a D-simplex amplitude

Showed the oscillatory part relates to the Regge action

Demonstrated the formalism's power in higher-dimensional models

Abstract

We show how spin networks can be described and evaluated as Feynman integrals over an internal space. This description can, in particular, be applied to the so-called simple SO(D) spin networks that are of importance for higher-dimensional generalizations of loop quantum gravity. As an illustration of the power of the new formalism, we use it to obtain the asymptotics of an amplitude for the D-simplex and show that its oscillatory part is given by the Regge action.