A gauge-covariant bimetric tetrad theory of gravitation and electromagnetism

In order to get to a geometrically based theory of gravitation and electromagnetism, a gauge covariant bimetric tetrad space-time is introduced. The Weylian connection vector is derived from the tetrads and it is identified with the electromagnetic potential vector. The formalism is simplified by the use of gauge-invariant quantities. The theory contains a contorsion tensor that is connected with spinning properties of matter. The electromagnetic field may be induced by conventional sources and by spinning matter. In absence of spinning matter, the equations are identical with those of the gauge-covariant bimetric theory.⁽²³⁾     

A unified theory of gravitation and electromagnetism for charged superfluids

We propose a unified theory of gravitation and electromagnetism which can be applied to charged multiply connected superfluids. It extends the conformally invariant Weyl-Dirac theory to complex gauge fields β and recovers flux quantization as the byproduct of a lagrangian constraint. Superconductors are described as multiply connected regions of space- time through the phase of β.     

Scale-covariant gravitation and electromagnetism

The theory of scale-covariant gravity is extended to include charged matter and electromagnetism at the classical level. The possibility of charge creation exists and the creation rate of charge differs from the creation rate of matter. A variational principle for scale-covariant gravity and electromagnetism coupled to a charged perfect fluid is given.Supported by a grant from the National Research Council of Canada.     

6-Optics and a general theory of gravitation and electromagnetism

It is shown that the equation of motion of material particles in a curved spacetime in the presence of electromagnetic field, known from general relativity, is equivalent to an equation for a geodesic line in a 6-dimensional Riemannian manifold of signature (+----+), at least when a special choice of the 6-metric has been made.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–40, December, 1984.     

Strings in a conformally invariant theory of gravitation and electromagnetism

A recently proposed unified theory of gravitation and electromagnetism is studied in the weak field approximation and conformally flat gauge. It requires the photon to have a mass real or imaginary (Meissner effect) depending on the sign of the cosmological constant λ, and proportional to λ^{$\text{1}\text{2}$}. Thus the range of the electromagnetic interaction must be greater than ～2 × 10²⁷ cm. The electromagnetic field is entirely of topological origin, strings are present in the theory and the flux of the electromagnetic field is quantized. A classical normalization condition for the potential makes the flux quantum equal to ± e, while the fine structure constant provides a scale for the rate of change in the length of a vector displaced around a closed path linking the flux.     

Physical geometry: A unified theory of gravitation,electromagnetism and other interactions

An invariant correlation and a variational principle are given for the theory of connections and frames introduced in previous papers. The relation of the resultant gravitation theory to Yang's theory is clarified. The resultant equations of motion, which imply a generalized Dirac equation, are used to understand geometrically certain aspects of relativistic quantum theory. The conjecture is proposed that electrornegnetism is related to anSU(2) subgroup. The possible association of the extra generators with strong and weak nuclear forces is discussed.     

Some electromagnetic consequences of a geometric unified theory of gravitation and electromagnetism

The geometrical unified theory of gravitation and electromagnetism discussed in previous publications requires that electromagnetism be represented by an SU(2) subgroup. Electric matter should correspond to irreducible representations of the structure group, SL(4,), induced from its compact subgroup, rotation SU(2)x electromagnetic SU(2). Results predict the quantization of electric charge, magnetic flux and angular momentum without requiring magnetic monopoles. Unexpectedly, the necessary quanta of charge and flux imply fractional quantization of transverse resistance, under certain conditions (Fractional Quantum Hall Effect).     

Complementary aspects of gravitation and electromagnetism

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge.     

Variational principle for theP(4) affine theory of gravitation and electromagnetism

We propose a Lagrangian for theP(4) theory of gravitation and electromagnetism which is a straightforward generalization of the Einstein Lagrangian. A constrained Palatini variation of this Lagrangian yields the geometrical Einstein-Maxwell affine field equations. We show that these results can be extended easily to include both electric and magnetic charges. Finally, we consider conservation laws arising from the invariance properties of the Lagrangian.     

New Weyl theory: Geometrization of electromagnetism and gravitation: Motivations and classical results

A geometrical unified field theory of electromagnetism and gravitation is developed in a Weyl space-time. The integrability conditions of the field equations cast the laws of classical perfect fluids under electromagnetic interactions. The purely gravitational limit of the theory is Einstein's General Relativity and the purely electromagnetic case coincides with the predictions of Maxwell's theory.     

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 _n → M _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 ³ R ₅⁴ with 1-dimensional fiber x ⁵ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry ³ V ₅⁴ with the general relativity pseudo-Riemannian space-time ³ V ₄, and 1-dimensional fiber x 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. The text was submitted by the author in English.     

A bi-metric theory of gravitation

A bi-metric theory of gravitation is proposed, satisfying the covariance and equivalence principles. It is based on a simple form of Lagrangian and has a simpler mathematical structure than that of the general theory of relativity. The theory agrees with general relativity up to the accuracy of the observations made up to now. The static spherically symmetric solution of the present field equations does not involve any 'black hole'.     

Unification of gravitation and electromagnetism with B(3)

The experimentally supported existence of the Evans Vigier field.B ⁽³⁾,in vacuo implies that the gravitational and electromagnetic fields can be unified within the same Ricci tensor, being respectively its symmetric and antisymmetric components in vacuo. The fundamental equations of motion of vacuum electromagnetism are developed in this framework.     

A scalar field theory of gravitation

A scalar theory of gravitation is developed from a variational principle. The speed of light is taken to be a function of the potential of the gravitational field. The predictions of the light deflection and the advancement of the perihelion agree with those made by Einstein's theory. The gravitational (active) mass differs from the inertial (passive) mass and both are dependent on the gravitational potential.     

Bianchi identities,electromagnetic waves,and charge conservation in theP(4) theory of gravitation and electromagnetism

The Bianchi identities for theP(4)=O(1, 3) ^4* theory of gravitation and electromagnetism are decomposed into the standardO(1, 3) Riemannian Bianchi identity plus an additional ^4* component. When combined with the Einstein-Maxwell affine field equations the ^4* components of theP(4) Bianchi identities imply conservation of magnetic charge and the wave equation for the Maxwell field strength tensor. These results are analyzed in light of the special geometrical postulates of theP(4) theory. We show that our development is the analog of the manner in which the Riemannian Bianchi identities, when combined with Einstein's field equations, imply conservation of stress-energy-momentum and the wave equation for the LanczosH-tensor.     

Gauge gravitation theory

The particularity of the gauge gravitation theory is that Dirac fermion fields possess only Lorentz exact symmetries. It follows that different tetrad gravitational fieldsh define nonisomorphic representations _h of cotangent vectors to a space-time manifoldX ⁴ by Dirac's-matrices on fermion fields. One needs these representations in order to construct the Dirac operator defined in terms of jet spaces. As a consequence, gravitational fieldsh fail to form an affine space modeled after any vector space of deviationsh'–h of some background fieldh. They therefore fail to be quantized in accordance with the familiar quantum field theory. At the same time, deformations of representation _h describe deviations ofh such thath + is not a gravitational field. These deviations form a vector space, i.e., satisfy the superposition principle. Their Lagrangian, however, differs from familiar Lagrangians of gravitation theory. For instance, it contains masslike terms.