SEMICLASSICAL LIMITS OF SIMPLICIAL QUANTUM-GRAVITY

We consider the simplicial state sum model of Ponzano and Regge as a p ath integral for quantum gravity in three dimensions. We examine the L orentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for 6j-symbols in terms of this g eometry. This extends Ponzano and Regge's similar interpretation for E uclidian geometry. We give a geometric interpretation of the stationar y points of this state sum, by showing that, at these points, the simp licial manifold may be mapped locally into flat Lorentzian or Euclidia n space. This lends weight to the interpretation of the state sum as a path integral, which has solutions corresponding to both Lorentzian a nd Euclidian gravity in three dimensions.