Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data

Understand

We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity.

• The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider.
• In particular, we study the asymptotic behavior of the path integral in the semi-classical limit.
• First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps.