the same paper those authors gave the first spin foam model (a discretized path integral) for quantum gravity. The formula of Ponzano and Regge is notable for its high symmetry and the manner in which it is related to the geometry of a tetrahedron in three-dimensional space. It is also remarkable because the phase of the asymptotic expression is identical to the Einstein-Hilbert action for three-dimensional gravity integrated over a tetrahedron, in Regge’s (1961) simplicial approximation to general relativity. The semiclassical limit of the $6j$-symbol thus plays a crucial role in simplicial approaches to the quantization of the gravitational field.

For all these reasons, the asymptotic formula of Ponzano and Regge for the $6j$-symbol has attracted a great deal of attention. Ponzano and Regge obtained their formula by inspired guesswork, supporting their conclusion both with numerical evidence and arguments of consistency and plausibility. The formula itself is of the one-dimensional WKB-type, a reflection of the fact that the $6j$-symbol fundamentally represents a dynamical system of one degree of freedom.

The Ponzano-Regge formula was first derived by Neville (1971), using the recursion relations satisfied by the $6j$-symbol and a discrete version of WKB theory. Similar techniques were later used by Schulten 