1997/04/06 by Fotini Markopoulou, Markopoulou, Fotini · 6 citations
Neuroscience · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Neural dynamics and brain function #Noncommutative and Quantum Gravity Theories #Quantum many-body systems #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9704013
Latex, 20 pages, 16 figures
arxiv created 1997/04/06 · openalex publication_date 1997/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We illustrate the relationship between spin networks and their dual representation by labelled triangulations of space in 2+1 and 3+1 dimensions. We apply this to the recent proposal for causal evolution of spin networks. The result is labelled spatial triangulations evolving with transition amplitudes given by labelled spacetime simplices. The formalism is very similar to simplicial gravity, however, the triangulations represent combinatorics and not an approximation to the spatial manifold. The distinction between future and past nodes which can be ordered in causal sets also exists here. Spacelike and timelike slices can be defined and the foliation is allowed to vary. We clarify the choice of the two rules in the causal spin network evolution, and the assumption of trivalent spin networks for 2+1 spacetime dimensions and four-valent for 3+1. As a direct application, the problem of the exponential growth of the causal model is remedied. The result is a clear and more rigid graphical understanding of evolution of combinatorial spin networks, on which further work can be based.