arXiv subjects

O. A. Olkhov

Publications and source records attributed to O. A. Olkhov.

7 recordsLinked to original sources

arXiv2008

On possibility of topological interpretation of quantum mechanics

Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. It is shown also that Dirac equation for hydrogen atom can be also considered as relation describing the space topological defect. Electromagnetic potentials appears within this approach as connectivities of the defect universal covering space and gauge invariance of electromagnetic field happens to be a natural consequence of topological interpretation. Proposed approach can be also considered as a nonlocal model with hidden variables. Preliminary results were published by parts early, and here they are presented completely.

physics.gen-ph↗

arXiv2007

Geometrization of quantum formalism

The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological manifolds). The Dirac equation for a hydrogen atom can also be interpreted as a relation that accounts for the symmetry properties of a piece of curved space. Within the framework of this concept, atoms have no any pointlike particles (electrons) inside, and the gauge invariance of electromagnetic field proves to be the natural consequence of the basic principles of the proposed geometrical approach.

quant-ph↗

arXiv2002

Topological interpretation of Dirac equation and geometrization of physical interactions

Earlier we have shown that interacting electron-positron and electromagnetic fields can be considered as a certain microscopic distortion of pseudo-Euclidean properties of the Minkovsky 4-space-time. The known Dirac and Maxwell equations prove to be group-theoretical relations describing this distortion (nonmetrized closed 4-manifold). Here we apply the above geometrical approach to obtain equations for a neutrino interacting with its weak field. These equations contain some new terms and demonstrate geometrical mechanisms of gauge-invariance and P-T violation. Equations are also proposed for gravitational field and its microscopic quantum sources.

hep-th↗

arXiv2002

Topological interpretation of Dirac equation and geometrisation of electromagnetic field

A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified closed connected nonmetrized space--time 4-manifold. Within this approach, the Dirac equation proves to be a group-theoretic relation that accounts for the topological and metric properties of this manifold. The Dirac spinors serve as basis functions of its fundamental group representation, while the tensor components of electromagnetic field prove to be the components of a curvature tensor of the relevant covering space. A basic distinction of the suggested approach from the geometrization of gravitational field in general relativity is that, first, not only the field is geometrized but also are its microscopic sources and, second, the field and its sources are treated not as a metrized Riemannian space--time but as a nonmetrized space-- time manifold. A possibility to geometrize weak interaction is also discussed.

hep-th↗

arXiv2002

Geometrisation of electromagnetic interaction

A new concept for the geometrisation of electromagnetic interaction is proposed. Instead of the concept "extended field--point sources", interacting Maxwell's and Dirac's fields are considered as a unified closed noneuclidean and nonriemannean space--time 4-manifold. This manifold can be considered as geometrical realisation of the "dressed electron" idea. Within this approach, the Dirac equation proves to be a relation that accounts for topological and metric characteristics of this manifold. Dirac's spinors serve as basis vectors of its fundamental group representation, while the electromagnetic field components prove to be components of a curvature tensor of the manifold covering space. Energy, momentum components, mass, charge, spin and particle--antiparticle states appear to be geometrical characteristics of the above manifold.

hep-th↗

arXiv2001

Geometrisation of electromagnetic field and topological interpretation of quantum formalism

A new approach is proposed for an electromagnetic field geometrisation. We show that interacting Maxwell and Dirac fields can be considered as a single connected space-time 4-manifold. The Dirac spinors appear wihtin such approach as basic fanctions for the manifold fundamental group representation and electric and magnertic fields appear as components of a curvature tensor of the manifold covering space.

quant-ph↗

arXiv2001

Geometrisation of quantum formalism

We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal symmetries within one symmetry group. We suppose that nonelectromagnetic interactions appear within such approach as the deviations of the metrics from the euclidian form. The expression for the long-range part of "effective" nucleon-nucleon potential is derived using this assumption.

quant-ph↗