Asymptotics of Relativistic Spin Networks

TL;DR

This paper derives asymptotic formulas for relativistic spin networks using stationary phase methods, connecting them to known 6j symbols and comparing with numerical results, with implications for quantum gravity models.

Contribution

It provides new asymptotic formulas for SO(4) and SO(3,1) relativistic spin networks, extending previous results and validating them through numerical comparisons.

Findings

Asymptotic formula for tetrahedral spin network matches the square of Ponzano-Regge 6j symbol

Derived asymptotics for 10j-symbols and compared with numerical calculations

Discussed implications for SO(3,1) spin network asymptotics

Abstract

The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the Spin Network evaluation. Finally we discuss the asymptotics of the SO(3,1) 10j-symbol.