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Alexey L. Krugly

Publications and source records attributed to Alexey L. Krugly.

8 recordsLinked to original sources
arXiv2014

A sequential growth dynamics for a directed acyclic dyadic graph

A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical self-organized structures of the graph without any reference to continuous spacetime. The dynamics of the model is considered. This dynamics is stochastic sequential additions of new vertexes. Growth of the graph is a Markovian process. This dynamics is a consequence of a causality principle.

gr-qc↗
arXiv2011

The dynamics of binary alternatives for a discrete pregeometry

A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the graph are added one by one. The probability of each step depends on the structure of existed graph. The particular case of dynamics is based on binary alternatives. Each directed path is considered as a sequence of outcomes of binary alternatives. The probabilities of a stochastic sequential growth are functions of these paths. The goal is to describe physical objects as some self-organized structures of the graph. A problem to find self-organized structures is discussed.

gr-qc↗
arXiv2011

An example of the stochastic dynamics of a causal set

An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures. The dynamics of this model is a stochastic sequential growth dynamics. New vertexes are added one by one. The probability of this addition depends on the structure of existed graph. The particular case of the dynamics is considered. The numerical simulation provides some symptoms of self-organization.

gr-qc↗
arXiv2011

Discrete mechanics: a sequential growth dynamics for causal sets that is based on binary alternatives

One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite partially ordered set. The dynamics of this model is a stochastic sequential growth dynamics. New elements of causal set are added one by one. The probability of this addition of a new element depends on the structure of existed causal set. The particular case of the dynamics is considered. This dynamics is based on binary alternatives. Each directed path is considered as a sequence of outcomes of binary alternatives. The probabilities of a stochastic sequential growth have quadratic dependence on these paths.

gr-qc↗
arXiv2010

Discrete mechanics: a kinematics for a particular case of causal sets

The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is introduced in [arXiv: 1004.5077]. These two papers introduce a consistent description of the model.

gr-qc↗
arXiv2010

Unfaithful embedding of causal sets

In the causal set approach, spacetime is a continuous approximation of a faithful embedded causal set. But the faithful embedded causal set describes the empty spacetime and cannot describe matter. Only faithful embedding of coarse grained causal set is necessary for the emergence of spacetime. The initial causal set can be unfaithfully embedded. The following properties of the universe can be the consequences of the unfaithful embedding: antiparticles, fields of interactions, the inhomogeneous distribution of the matter.

physics.gen-ph↗
arXiv2010

Discrete mechanics: a sequential growth dynamics for causal sets, and a self-organization of particles

A model of a discrete pregeometry on a microscopic scale is introduced. This model is a finite network of finite elementary processes. The mathematical description is a d-graph that is a generalization of a graph. This is the particular case of a causal set. The aim of this study is to construct the particles as emergent structures. The particles in this model must be cyclic processes. The general dynamics and several examples are given. A simple dynamics generates a hierarchy of cyclic processes. An algebraic representation of this dynamics is given. It is based on the algebra of creation and destruction operators. Loops are described by bosonic operators and causal connections are described by fermionic operators.

gr-qc↗