The R.I. Pimenov unified gravitation and electromagnetism field theory as semiRiemannian geometry
Abstract
More than forty years ago R.I. Pimenov introduced a new geometrysemiRiemannian oneas a set of geometrical objects consistent with a fibering pr: M{sub n} {yields} M{sub m}. He suggested the heuristic principle according to which the physically different quantities (meter, second, Coulomb, etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudoRiemannian one, a multiplefibered semiRiemannian geometry is the most appropriate one for the treatment of more than three different physical quantities as unified geometrical field theory. SemiEuclidean geometry {sup 3}R{sub 5}{sup 4} with 1dimensional fiber x{sup 5} and 4dimensional Minkowski spacetime as a base is naturally interpreted as classical electrodynamics. SemiRiemannian geometry {sup 3}V{sub 5}{sup 4} with the general relativity pseudoRiemannian spacetime {sup 3}V{sub 4}, and 1dimensional fiber x{sup 5}, responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike KaluzaKlein theories, where the fifth coordinate appears in nondegenerate Riemannian or pseudoRiemannian geometry, the theory based on semiRiemannian geometry is free from defects of the former. In particular, scalar field does not arise.
 Authors:
 Komi Science Center UrD RAS, Department of Mathematics (Russian Federation)
 Publication Date:
 OSTI Identifier:
 21405931
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Atomic Nuclei; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1134/S106377880905007X; Copyright (c) 2009 Pleiades Publishing, Ltd.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; ELECTRODYNAMICS; ELECTROMAGNETISM; EUCLIDEAN SPACE; GENERAL RELATIVITY THEORY; GRAVITATION; KALUZAKLEIN THEORY; MINKOWSKI SPACE; ONEDIMENSIONAL CALCULATIONS; RIEMANN SPACE; SCALAR FIELDS; SPACETIME; FIELD THEORIES; MAGNETISM; MATHEMATICAL SPACE; RELATIVITY THEORY; SPACE; UNIFIEDFIELD THEORIES
Citation Formats
Gromov, N. A., Email: gromov@dm.komisc.r. The R.I. Pimenov unified gravitation and electromagnetism field theory as semiRiemannian geometry. United States: N. p., 2009.
Web. doi:10.1134/S106377880905007X.
Gromov, N. A., Email: gromov@dm.komisc.r. The R.I. Pimenov unified gravitation and electromagnetism field theory as semiRiemannian geometry. United States. doi:10.1134/S106377880905007X.
Gromov, N. A., Email: gromov@dm.komisc.r. 2009.
"The R.I. Pimenov unified gravitation and electromagnetism field theory as semiRiemannian geometry". United States.
doi:10.1134/S106377880905007X.
@article{osti_21405931,
title = {The R.I. Pimenov unified gravitation and electromagnetism field theory as semiRiemannian geometry},
author = {Gromov, N. A., Email: gromov@dm.komisc.r},
abstractNote = {More than forty years ago R.I. Pimenov introduced a new geometrysemiRiemannian oneas a set of geometrical objects consistent with a fibering pr: M{sub n} {yields} M{sub m}. He suggested the heuristic principle according to which the physically different quantities (meter, second, Coulomb, etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudoRiemannian one, a multiplefibered semiRiemannian geometry is the most appropriate one for the treatment of more than three different physical quantities as unified geometrical field theory. SemiEuclidean geometry {sup 3}R{sub 5}{sup 4} with 1dimensional fiber x{sup 5} and 4dimensional Minkowski spacetime as a base is naturally interpreted as classical electrodynamics. SemiRiemannian geometry {sup 3}V{sub 5}{sup 4} with the general relativity pseudoRiemannian spacetime {sup 3}V{sub 4}, and 1dimensional fiber x{sup 5}, responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike KaluzaKlein theories, where the fifth coordinate appears in nondegenerate Riemannian or pseudoRiemannian geometry, the theory based on semiRiemannian geometry is free from defects of the former. In particular, scalar field does not arise.},
doi = {10.1134/S106377880905007X},
journal = {Physics of Atomic Nuclei},
number = 5,
volume = 72,
place = {United States},
year = 2009,
month = 5
}

Unified theory of gravitation, electromagnetism, and the YangMills field
The recent modification and extension of Einstein's nonsymmetric unified field theory for gravitation and electromagnetism is generalized to include the YangMills field theory. The generalization consists in assuming that the components of the linear connection and of the fundamental tensor are not ordinary c numbers but are matrices related to some unitary symmetry. As an example we consider the SU(2) case. The theory is applied to the gaugecovariant formulation of electrically and isotopically charged spin1/2 field theories. (AIP) 
Unified gauge theory for electromagnetism and gravitation based on twistor bundles
A unified gauge theory of the combined gravitational and electromagnetic fields is obtained by two different procedures using twistors as a starting point for the construction of the appropriate bundles. One of these formalisms is obtained by relaxing the conditions on the structure of a twistor bundle theory previously developed by the authors for the Poincare group as the structure group. The other formalism is based on a tensor product bundle and can be readily extended to include structure groups involving direct products of nonabelian groups with the Poincare group. The results of the theory are compared with those obtainedmore » 
Unified YangMills theory of gravitation and electromagnetism
The group properties of a new unified field theory of gravitation and electromagnetism are studied within a YangMills scheme using a complex tetrad formalism. (AIP)