The discrete model of spacetime and the binary pregeometry of vladimirov

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The discrete model of spacetime is considered. This is a finite connected directed acyclic graph. The indegree and the outdegree of each vertex is no more than 2. Then this graph is called x-graph. Vertices are elementary events. Edges are elementary causal relations. Vertices and edges are nondivisible. They have no intrinsic properties. All properties are the topology of x-graph. The world line of elementary particle is considered as a sequence of repetetive structures. There are two tasks. The first is a dynamics of x-graph. This task is not considered. The second task is the identification of topological structures and phisical objects, topological properties and phisical quantities. To solve this task we need a correspondence the topology of x-graph and quantum discription. In quantum discription we use complex numbers. In topology of x-graph we use natural numbers as the number of vertices, the number of edges, the number of some pathes and so on. We get complex numbers for topology of x- graph by Fourier analysis. Some properties of x-graph are proved. Using these properties the topology of x-graph can be described by binary systems of complex relations of Vladimirov. We can use the results of Vladimirov for analysis and physical interpretation of x-graph topology.

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Directed acyclic graph, fourier analysis, binary systems of complex relations

Короткий адрес: https://sciup.org/142221700

IDR: 142221700   |   DOI: 10.17238/issn2226-8812.2019.2.15-27

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