The Ponzano-Regge asymptotic of the 6j symbol: an elementary proof

TL;DR

This paper provides a straightforward proof of the Ponzano-Regge asymptotic formula for the Wigner 6j symbol, unifying treatment of half-integer and integer spins, with implications for spin foam models.

Contribution

It offers an elementary, direct proof of the asymptotic formula starting from Racah's single sum, including a generalization to Minkowskian tetrahedra.

Findings

Unified treatment of half-integer and integer spins.

Direct generalization to Minkowskian tetrahedra.

Potential impact on renormalization in spin foam models.

Abstract

In this paper we give a direct proof of the Ponzano-Regge asymptotic formula for the Wigner 6j symbol starting from Racah's single sum formula. Our method treats halfinteger and integer spins on the same footing. The generalization to Minkowskian tetrahedra is direct. This result should be relevant for the introduction of renormalization scales in spin foam models.