skip to main content

Title: The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

More than forty years ago R.I. Pimenov introduced a new geometry-semi-Riemannian one-as 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 pseudo-Riemannian one, a multiple-fibered semi-Riemannian geometry is the most appropriate one for the treatment of more than three different physical quantities as unified geometrical field theory. Semi-Euclidean geometry {sup 3}R{sub 5}{sup 4} with 1-dimensional fiber x{sup 5} and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry {sup 3}V{sub 5}{sup 4} with the general relativity pseudo-Riemannian space-time {sup 3}V{sub 4}, and 1-dimensional fiber x{sup 5}, responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the fifth coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise.
Authors:
 [1]
  1. 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; KALUZA-KLEIN THEORY; MINKOWSKI SPACE; ONE-DIMENSIONAL CALCULATIONS; RIEMANN SPACE; SCALAR FIELDS; SPACE-TIME FIELD THEORIES; MAGNETISM; MATHEMATICAL SPACE; RELATIVITY THEORY; RIEMANN SPACE; SPACE; UNIFIED-FIELD THEORIES