Discrete space-time
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.
scientific article; zbMATH DE number 1529016