, Volume 41, Issue 1, pp 1-37

Causal Set Dynamics and Elementary Particles

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A causal set is considered a finite, acyclic oriented graph with special restrictions: each vertex has two incident edges directed to this vertex and two incident edges directed from this vertex. This graph is called a causal graph. The vertex with incident edges is called an X-structure. Quantum measurements are discussed. A dynamics of the causal graph is a random sequence of elementary interactions of edges that is described by complex amplitudes. These amplitudes correspond to each pair of interacting edges. The edges are elementary particles. The mass of a particle is a probability of the interaction. An equation of particles is proposed. In a simple case this equation for X-structure is the Dirac's equation. The edges are fermions with the spin 1/2.