A Step Toward Pregeometry I.: Ponzano-Regge Spin Networks and the Origin of Spacetime Structure in Four Dimensions

Details A Step Toward Pregeometry I.: Ponzano-Regge Spin Networks and the Origin of Spacetime Structure in Four Dimensions A Step Toward Pregeometry I.: Ponzano-Regge Spin Networks and the Origin of Spacetime Structure in Four Dimensions

1993-10-26

arxiv.org/abs/gr-qc/9310036v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

57 pages + 20 shar'ed, uuencoded, compressed eps figures, no local preprint number

Scientific paper

In this paper, a candidate for pregeometry, Ponzano-Regge spin networks, will be examined in the context of the pregeometric philosophy of Wheeler. Ponzano and Regge were able to construct a theory for 3-dimensional quantum gravity based on 3nj-symbols, obtaining the path integral over the metric in the semiclassical limit. However, extension of this model to 4-dimensions has proven to be difficult. It will be shown that the building blocks for 4-dimensional spacetime are already present in the Ponzano-Regge formalism using a reinterpretation of the theory based on the pregeometric hypotheses of Wheeler.

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