arXiv subjects

A. L. Koshkarov

Publications and source records attributed to A. L. Koshkarov.

4 recordsLinked to original sources

arXiv2009

The Levi-Civita tensor noncovariance and curvature in the pseudotensors space

It is shown that conventional "covariant" derivative of the Levi-Civita tensor is not really covariant. Adding compensative terms, it is possible to make it covariant and to be equal to zero. Then one can be introduced a curvature in the pseudotensors space. There appears a curvature tensor which is dissimilar to ordinary one by covariant term including the Levi-Civita density derivatives hence to be equal zero. This term is a little bit similar to Weylean one in the Weyl curvature tensor. There has been attempted to find a curvature measure in the combined (tensor plus pseudotensor) tensors space. Besides, there has been constructed some vector from the metric and the Levi-Civita density which gives new opportunities in geometry.

physics.gen-ph↗

arXiv2006

Nonabelian duality and analytic continuation of instantons

Within the framework of the gauge O(1,3)\times O(1,3)-theory, an extension of the Belavin-Polyakov-Schwarz-Tyupkin ansatz is proposed by incorporation there the Levi-Civita tensor. The duality properties of the theory, admitting introduction the complex structure, are such that selfduality condition of the field tensor is an equation for complex-analytic function. New type of duality is found out.

hep-th↗

arXiv2004

On General Relativity extension

The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills' equations for the curvature tensor. Einstein's equations (with cosmological term to appear as an integration constant) are contained in the theory proposed. New is that now gravitational field is not exceptionally determined by matter energy-momentum but can possess its own non-Einsteinian dynamics(vacuum fluctuations, self-interaction)which is generally an attribute of nonabelian gauge field. The gravitational equations proper due to either matter energy-momentum or vacuum fluctuations are side conditions imposed on the Riemann tensor, like self-duality conditions.

gr-qc↗

arXiv1997

Dual Symmetry in Gauge Theories

Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang--Mills equations have. An Abelian two-parameter dual group is found to exist in Gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real) solutions to the usual duality equations. Central-symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein's equations. However, the theory obtained reduces to the conformal-flat Nordstrom theory.

hep-th↗