Quanta of Space-Time and Axiomatization of Physics
Abstract
We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation relation in dimension 4 implies volume quantization and determines a noncommutative space which is a tensor product of continuous and discrete spaces. This noncommutative space predicts the full structure of a unified model of all particle interactions based on Pati-Salam symmetries or, as a special case, the Standard Model. We study implications of this quantization condition on Particle Physics, General Relativity, the cosmological constant and dark matter. We demonstrate that, with little input, noncommutative geometry gives a compelling and attractive picture about the nature and structure of space-time.
Keywords
Cite
@article{arxiv.1702.08180,
title = {Quanta of Space-Time and Axiomatization of Physics},
author = {Ali H. Chamseddine},
journal= {arXiv preprint arXiv:1702.08180},
year = {2018}
}
Comments
47 pages. Contribution to the special issue of IJGMMP celebrating the one century anniversary of the program announced in 1916 by Hilbert entitled " Foundations of Mathematics and Physics", editors, Joseph Kouneiher, John Stachel and Salvatore Capozzieolo