A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces

Abstract

We reformulate the Ponzano-Regge quantum gravity model in terms of surfaces on a 3-dimensional simplex lattice. This formulation (1) has a clear relation to the loop representation of the canonical quantum general relativity in 3-dimensions, (2) may have a 4-dimensional analogue, in contrast to the 6-j symbolic formalism of the Ponzano-Regge model, and (3) is purely a theory of surfaces, in the sense that it does not include any field variables; hence it is coordinate-free on the surface and background-free in spacetime. We discuss implications and applications of this formulation.