Discrete space-time

Abstract

A variant of the causal set hypothesis is discussed. Discrete space-time is an oriented graph, and the vertexes of the graph are world points. The oriented edges are elementary causal connections. The graph is the deepest level of matter. The vertexes and the edges are elementary objects and have no internal structure. All information consists in the structure of the graph, which is described by sums of paths. Grassmann variables and integrals of Grassmann variables are used for summing paths. The sums of paths define complex amplitudes, which correspond to each pair of vertexes. The complex amplitudes of all pairs of vertexes comprise a Hermitian amplitude matrix.