Quantum Space-Time as a Quantum Causal Set
摘要
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.
引用
@article{arxiv.gr-qc/0201004,
title = {Quantum Space-Time as a Quantum Causal Set},
author = {Ioannis Raptis},
journal= {arXiv preprint arXiv:gr-qc/0201004},
year = {2007}
}
备注
8 pages, ReV-TeX, substantially revised, expanded and updated version