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

1993/10/26 by Norman J. LaFave, LaFave, Norman J. · 3 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.gr-qc/9310036

openalex publication_date 1993/10/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Quantum process and the foundation of relational theories of space-time
• The Small Scale Structure of Space-Time: A Bibliographical Review
• The arrangement field of the space-time points

Related

• Spin networks in quantum gravity
• On a Pregeometric Origin for Spacetime Dimensionality and Metric Structure
• Quantum mechanics and gravity as preclusion principles of four dimensional geometries
• A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces
• Further simplification of the constraints of four-dimensional gravity