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Yuri A. Rylov

Publications and source records attributed to Yuri A. Rylov.

63 records · Page 4Linked to original sources
arXiv2001

Dynamic disquantization of Dirac equation

Classical model S_dc of Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. Its classical analog S_dc is described by a system of ordinary differential equations, containing the quantum constant h as a parameter. Dynamic equations for S_dc are determined by the Dirac equation uniquely. Both dynamic systems S_D and S_dc appear to be nonrelativistic. One succeeded in transforming nonrelativistic dynamic system S_dc into relativistic one S_dcr. The dynamic system S_dcr appears to be a two-particle structure (special case of a relativistic rotator). It explains freely such properties of S_D as spin and magnetic moment, which are strange for pointlike structure. The rigidity function f_r(a), describing rotational part of total mass as a function of the radius $a$ of rotator, has been calculated for S_dcr. For investigation of S_D and construction of S_dc one uses new dynamic methods: dynamic quantization and dynamic disquantization. These relativistic pure dynamic procedures do not use principles of quantum mechanics (QM). They generalize and replace conventional quantization and transition to classical approximation. Totality of these methods forms the model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle and effective, than conventional methods of QM. MCQP relates to conventional QM, much as the statistical physics relates to thermodynamics.

quant-ph↗
arXiv2001

Pair production problem and canonical quantization of nonlinear scalar field in terms of world lines

A new quantization scheme (WL-scheme), using world lines as objects of quantization, is proposed. Applying to nonlinear scalar field, the WL -scheme is investigated and compared with the conventional PA-scheme of quantization. In the PA-scheme objects of quantization are particles and antiparticles, which are fragments of the total physical object -- world line (WL). Applying to the nonlinear field, the PA-scheme of quantization leads to such difficulties as nonstationary vacuum, obligatory use of perturbation theory technique, normal ordering and cut-off in the scattering problem. These difficulties are corollaries of inconsistency of PA-scheme. The WL-scheme is free of these difficulties. These difficulties are connected with the reconstruction problem of the total world lines from their fragments (particles and antiparticles). In the case, when these fragments interact between themselves, such a reconstruction is very complicated problem. The new WL-scheme of quantization is free of all these problems, because it does not cut the total world line into fragments (particles and antiparticles). Formally appearance of fragments in the conventional quantization PA-scheme is a corollary of identification of the energy with the Hamiltonian. In fact such an identification is not necessary. It leads only to difficulties. The new WL-scheme of quantization does not use this identification and enables to go around all these problems. The WL-scheme enables not to use additional (to nonrelativistic QM) quantization rules, used in the relativistic QFT (normal ordering, perturbation technique, renormalization).

hep-th↗
arXiv2001

Ptolemyness of conventional program for microcosm investigations and alternative research program

It is shown that the conventional approach to microcosm investigations uses an incorrect supposition (incorrect space-time model) whose incorrectness is compensated by means of additional hypotheses, known as quantum mechanics principles. Such a conception reminds the Ptolemaic doctrine of celestial mechanics. Alternative research program, which uses a more correct space-time model and does not need additional hypotheses (quantum principles) for free explanations of quantum effects, is suggested. If the more correct space-time model were known in the beginning of XXth century, when research of microcosm started, quantum mechanics could develop in other way. The alternative research program appeared with a secular delay, because all this time the necessary mathematical technique was not available for researchers. Absence of necessary mathematical technique is connected with some prejudices which have been overcame at the construction of new conception of geometry and that of statistical description. Basic statements of the new mathematical technique and principles of its application in alternative research program are presented in the paper.

quant-ph↗
arXiv2001

Geometry without topology as a new conception of geometry

A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T-geometric one. T-geometry is the simplest geometric conception (essentially only finite point sets are investigated) and simultaneously it is the most general one. It is insensitive to the space continuity and has a new property -- nondegeneracy. Fitting the T-geometry metric with the metric tensor of Riemannian geometry, one can compare geometries, constructed on the basis of different conceptions. The comparison shows that along with similarity (the same system of geodesics, the same metric) there is a difference. There is an absolute parallelism in T-geometry, but it is absent in the Riemannian geometry. In T-geometry any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T-geometric conception appears to be more consistent logically, than the Riemannian one.

math.MG↗
arXiv2000

Hamilton Variational Principle for Statistical Ensemble of Deterministic Systems and its Application for Ensemble of Stochastic Systems

Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and provides a basis for a description of statistical ensemble of stochastic systems. It is shown that sometimes such a statistical description of stochastic particle motion appears to coincide with the quantum description in terms of Schroedinger equation.

math-ph↗
arXiv2000

Geometry without Topology

The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties. For instance, the straight, passing through points A and B, is defined as a set of such points R that the area S(A,B,R) of the triangle ABR vanishes. The triangle area is expressed via metric by means of the Hero's formula, and the straight appears to be defined only via metric, i.e. without a reference to (topological) concept of curve. (Usually the straight is defined as the shortest curve, connecting two points A and B). Such a construction of geometry is free from constraints (continuity, dimensionality of space), generated by a use of topology, but not by geometry in itself. At such a description all information on the geometry properties (such as uniformity, isotropy, continuity and degeneracy) is contained in metric. Modifying the metric, one changes the geometry automatically. The Riemannian geometry is constructed by two different ways: (1) by conventional way on the basis of metric tensor, (2) as a result of modification of the metric in the sigma-immanent description of the proper Euclidean geometry. The two obtained geometries are compared. The convexity problem in geometry and the problem of collinerity of vectors at distant points are considered. The nonmetric definition of curve is shown to be a concept of only proper Euclidean geometry. It is inadequate to any non-Euclidean geometry.

math.MG↗
arXiv1999

Integration of Complete System of Dynamic Equations for Ideal Fluid

The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The complete system of dynamic equations for the ideal fluid can be integrated. Description in terms of hydrodynamic potentials (DTHP) arises as a result of this integration. The integrated system contains indefinite functions of three arguments, which can be expressed via initial and boundary conditions. The remaining initial and boundary conditions for the integrated system can be made universal (i.e. the same for all fluid flows), and the resulting system of equations contains full information about the fluid flow including initial and boundary conditions for the fluid flow. Some hydrodynamic potentials appear to be frozen into the fluid, and the Kelvin's theorem on the velocity circulation can be formulated in a contour-free form. Description in terms of the wave function (DTWF) appears to be a kind of DTHP. Calculation of slightly rotational flows can be carried out on the basis of DTHP, or DTWF. Such a description of a rotational flow appears to be effective.

physics.flu-dyn↗
arXiv1999

Classification of Finite Subspaces of Metric Space Instead of Constraints on Metrics

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only metric. It admits to remove constraints imposed usually on metric (the triangle axiom and nonnegativity of the squared metric), and to use the metric space for description of the space-time and other geometries with indefinite metric. Describing space-time and using this method, one can explain quantum effects as geometric effects, i.e. as space-time properties

math.MG↗