Related papers: Geometrization of Classical Wave Fields
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…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
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…
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…
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…
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…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
In the present paper a geometrization of electrodynamics is proposed which makes use of a generalization of Riemannian geometry considered already by Einstein and Cartan in the 20ies. Cartan's differential forms description of a…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
The appealing connection between non-Euclidean geometries and defects in solids is brought forth in this article. Drawing a correspondence between the nature of a defect and a specific geometric property of the material space not only…
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior…
The waves of fermions display nonlocality in low energy limit of quantum fields. In this \QTR{it}{ab initio} paper we propose a complex-geometry model that reveals the affection of nonlocality on the interaction between material particles…
We argue that the topological structure of Abelian gauge theories, such as Maxwell electrodynamics, in the background of a Euclidean Schwarzschild black hole manifests itself through an asymmetry in Hawking radiation. In particular, the…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
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…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…