scholarly journals An Interpretation of the Field Tensor in the Unified Field Theory

1954 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
NW Taylor
Keyword(s):  
Field Theory ◽  
Current Density ◽  
Free Space ◽  
Spherically Symmetric ◽  
Symmetric Part ◽  
Field Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field ◽  
Electric And Magnetic Fields

It is assumed that the skew symmetric part of the field tensor gik is a complex, self-dual tensor. This permits the whole set of field equations for free space to be derived directly from the theory without the introduction of an electric current density tensor. However, with this assumption it appears impossible for spherically symmetric electric and magnetic fields to exist in free space.

scholarly journals A Field Theory with Curvature and Anticurvature

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. I. Wanas ◽  
Mona M. Kamal
Keyword(s):  
Field Theory ◽  
Free Space ◽  
Unified Field Theory ◽  
Field Equations ◽  
Weak Equivalence Principle ◽  
Unified Field ◽  
Special Cases ◽  
Geometric Objects ◽  
Pure Gravity ◽  
Physical Quantities

The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

scholarly journals Six-dimensional considerations of Einstein's connection for the first two classes. II. The Einstein's connection in6-g-UFT

1999 ◽  
Vol 22 (3) ◽  
pp. 483-488
Author(s):  
Kyung Tae Chung ◽  
Gye Tak Yang ◽  
In Ho Hwang
Keyword(s):  
Field Theory ◽  
Recurrence Relations ◽  
Sufficient Condition ◽  
Field Tensor ◽  
Necessary And Sufficient Condition ◽  
Unified Field Theory ◽  
The Third ◽  
Unified Field ◽  
Necessary And Sufficient ◽  
Lower Dimensional

Lower dimensional cases of Einstein's connection were already investigated by many authors forn=2,3,4,5. In the following series of two papers, we present a surveyable tensorial representation of6-dimensional Einstein's connection in terms of the unified field tensor:I. The recurrence relations in6-g-UFT.II. The Einstein's connection in6-g-UFT.In our previous paper [2], we investigated some algebraic structure in Einstein's6-dimensional unified field theory (i.e.,6-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in6-g-UFT. This paper is a direct continuation of [2]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in6-g-UFT and to display a surveyable tensorial representation of6-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [2].All considerations in this paper are restricted to the first and second classes of the6-dimensional generalized Riemannian manifoldX6, since the case of the third class, the simplest case, was already studied by many authors.

The static spherically symmetric solutions in a unified field theory

1957 ◽  
Vol 53 (2) ◽  
pp. 489-493 ◽  
Author(s):  
John Moffat
Keyword(s):  
Charged Particle ◽  
Electric Energy ◽  
Gravitational Theory ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Fundamental Properties ◽  
Unified Field ◽  
Conditions At Infinity

ABSTRACTA brief account is given of the fundamental properties of a new generalization ((1), (2)) of Einstein's gravitational theory. The field equations are then solved exactly for the case of a static spherically symmetric gravitational and electric field due to a charged particle at rest at the origin of the space-time coordinates. This solution provides information about the gravitational field produced by the electric energy surrounding a charged particle and yields the Coulomb potential field. The solution satisfies the required boundary conditions at infinity, and it reduces to the Schwarzschild solution of general relativity when the charge is zero.

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1932 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Axial Symmetry ◽  
Unified Field Theory ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Unified Field ◽  
Theory Of Gravitation

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

Treatment of a static spherically symmetric matter distribution on the basis of the projective unified field theory

1990 ◽  
Vol 311 (6) ◽  
pp. 343-350 ◽  
Author(s):  
R. M. Avakian ◽  
E. V. Chubarian ◽  
A. V. Sarkissian ◽  
E. Schmutzer
Keyword(s):  
Field Theory ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Matter Distribution ◽  
Unified Field
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