Discrete space-time
type: Item
instance of: scholarly article
title: Discrete space-time
zbMATH Open document ID: 0972.83027
DOI: 10.1023/A:1003659805483
author: Alexey L. Krugly
published in: International Journal of Theoretical Physics
publication date: 2001-11-16T00:00:00Z
review text: The main contents of this paper is the causal set hypothesis, describing spacetime as a discrete, locally finite, partially ordered set aiming on the mathematical description via graph theory. The model of spacetime as a graph is introduced and the principle properties are discussed (causality, particles as parts of graphs, vertexes are the discrete analogues of points of continuous spacetime etc.). The only restriction is the causality principle. The relations and the description of graphs as the discrete counterpart to path integrals are introduced. The elements of the incidence matrix are interpreted as generators of a Grassmann algebra. Several special cases are discussed to obtain the correct description of path integrals as quantum mechanical tools. It is shown that an amplitude matrix, which should correspond to an elementary particle (or fragments of the graph) is a Hermitian matrix.
reviewed by: Thoralf Chrobok
Mathematics Subject Classification ID: 83C27
Mathematics Subject Classification ID: 52C99
Mathematics Subject Classification ID: 83A05
zbMATH DE Number: 1529016
zbMATH Keywords: discrete spacetime
zbMATH Keywords: graph theory
zbMATH Keywords: causal set hypothesis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1529016