Coherent states for canonical quantum general relativity and the infinite tensor product extension

We summarize a recently proposed concrete programme for investigating the ( semi)classical limit of canonical, Lorentzian, continuum quantum general re lativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an I nfinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite v olume (thermodynamic) limit of the theory which has been out of reach so fa r. (C) 2001 Elsevier Science B.V. All rights reserved.