2002/01/02 by I. Raptis, Ioannis Raptis, Raptis, Ioannis
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.gr-qc/0201004
8 pages, ReV-TeX, substantially revised, expanded and updated version
openalex publication_date 2002/01/02 · arxiv created 2002/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically interpreted as a locally finite, causal and quantal version of the kinematical structure of general relativity: the 4-dimensional Lorentzian space-time manifold and its continuous local orthochronous Lorentz symmetries. We discuss various possible dynamical scenarios for quantum causal sets mainly by using sheaf-theoretic ideas, and we entertain the possibility of constructing an inherently finite and genuinely smooth space-time background free quantum theory of gravity. At the end, based on the quantum causal set paradigm, we anticipate and roughly sketch out a potential future development of a noncommutative topology, sheaf and topos theory suitable for quantum space-time structure and its dynamics.