Transposition-invariant equations for the unified field theory

We discuss, within the framework provided by a recently developed variational method, transposition-invariant field equations for unified field theories. Systems that are, in addition, invariant under Weyl-type gauge transformations or lambda transformations are derived. It is found that in a weak field limit two of the systems contain the equations of general relativity and the covariant Maxwell equations for a charge-free region.     

On the strength of Einstein's unified field equations

Einstein's concept of the strength of a system of field equations, which has been related in a simple way to the amount of initial data required for the system, is examined for his last unified field theory. The apparently surprising weakness of this system is traced to the high order of the associated electromagnetic field equations. These equations allow the existence of purely electric longitudinal waves, in spite of the absence of any photon mass.     

New field equations in the 5-dimensional projective unified field theory

New field equations of the Projective Unified Field Theory are presented which avoid potential difficulties of former versions with respect to the equivalence principle. The physical interpretation of this new version remains unchanged: constancy of the “gravitational constant”, electromagnetic polarization of the vacuum, definiteness of the energy of the stationary scalaric field, etc. Furthermore, the Klein-Gordon field and the Dirac field are treated.     

Geometry of the submanifolds of SEXn. II. The generalized fundamental equations for the hypersubmanifold of SEXn

A connection which is both Einstein and semisymmetric is called an SE connection, and a generalizedn-dimensional Riemannian manifold on which the differential geometric structure is imposed byg through an SE connection is called ann-dimensional SE manifold and denoted by SEX_n. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEX_n, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.     

Structural equations for generalized killing-yano tensors

The so-called structural equations for generalized Killing-Yano tensors are derived. The first set of integrability conditions for the structural equations are also obtained. Several consequences of the integrability conditions are then discussed. For instance, it is shown that the maximal number of generalized Killing-Yano tensors occurs in flat space.Work done under the auspices of the National Group for Mathematical Physics of C.N.R.     

Considerations on a unified field theory

A geometrical formulation of gravitational and electromagnetic fields is presented for systems composed of point mass charged particles where the charge is small enough that electromagnetic radiation may be neglected. It is assumed that such charges produce a non-negligible contribution to the metric, and that their motion describes geodesics in the total metric which consists of that due to the charge itself and that due to the external environment of the charge. The above, together with several other assumptions yields the customary Einstein-Maxwell relations. It is demonstrated that this construction is not merely a re-statement of the Einstein-Maxwell theory in different terms.     

The nonsymmetric unified field theory

This paper reviews the recent progress in the nonsymmetric unified field theory of Einstein and Straus and its current status as a theory of macrophysics of gravitation and electromagnetism.     

General relativity without tensors in a central field

For static and spherically symmetric gravitational fields in the general theory of relativity, it is found possible completely to avoid tensor analysis. The principle of equivalence, illustrated by Einstein's elevator, is used to obtain Schwarzschild's equation, on which the three well-known tests of the general theory are usually based. The derivation is guided, as with Einstein, by Poisson's (Laplace's, in empty space) equation, which here can be solved by simple calculus.     

Quartic equations and classification of Riemann tensors in general relativity

For space-times in general relativity, the Petrov classification of the Weyl conformai curvature and the Plebaski or Segre classification of the Ricci tensor each depend on the properties of the roots of quartic equations. The coefficients in these quartic equations are in general complicated functions of the space-time coordinates. We review the general theory of quartic equations, and discuss algorithms for determining the existence and values of multiple roots. We consider practical implementation of an algorithm and the consequent Petrov classification. Tests of programs embodying this algorithm, using the computer algebra system CLASSI based on SHEEP, are reported.     

Space tensors in general relativity III: The structural equations

A self-consistent theory of spatial differential forms over a pair (M,Γ)is proposed. The operators d(spatial exterior differentiation), d_T (temporal Lie derivative) andL (spatial Lie derivative) are defined, and their properties are discussed. These results are then applied to the study of the torsion and curvature tensor fields determined by an arbitrary spatial tensor analysis \((\tilde \nabla ,\tilde \nabla T)\) (M,Γ). The structural equations of \((\tilde \nabla ,\tilde \nabla T)\) and the corresponding spatial Bianchi identities are discussed. The special case \((\tilde \nabla ,\tilde \nabla T) = (\tilde \nabla *,\tilde \nabla T*)\) is examined in detail. The spatial resolution of the Riemann tensor of the manifold M is finally analysed; the resultingstructure of Eintein's equations over a pair (ν₄,Γ)is established. An application to the study of the problem of motion in terms of co-moving atlases is proposed.     

A question concerning unified field theory

The quantum hydrodynamics of extended particles is advanced by taking into account the gravitational field. A system of equations is obtained for relativistic nonlinear quantum unified field theory.Institute of Terrestrial Magnetism, the Ionosphere and Radiowave Propagation, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–76, November, 1993.     

Electromagnetic effects in unified field theory

In unified field theory we derive expressions for the electric current densities j and. We show that j and depend on the intensitiesE andH;E andH possess a common limit 1/; and Coulomb's law is not compatible with the unified theory.     

A unified mechanism for experiments on ultrasonic field visualization

The acceleration of chemical reactions due to an ultrasonic field is the basis of a number of methods for the visualization of this field. Such methods have been examined with qualitative and quantitative experiments to determine the mechanism of ultrasonic action. It is found that the standing wave created by reflection of the ultrasound acts upon a diluted substance. The substance is concentrated at the displacement nodes of the standing wave and consequently in these regions the reaction is accelerated. An explanation is also given for some previous experiments.     

External field of a localized charge in unified field theory

The possibility of the existence of localized charged distribution giving rise to a special axially symmetric electrostatic field has been explored in Einstein's unified field theory [2]. The field equations have been studied in two particular cases. In one case the field equations have a solution representing flat space-time along with an electrostatic field which is constant in the direction of the axis of symmetry. For the other case the solution is non-existent.     

Covariant extensions and the nonsymmetric unified field

The problem of generally covariant extension of Lorentz invariant field equations, by means of covariant derivatives extracted from the nonsymmetric unified field, is considered. It is shown that the contracted curvature tensor can be expressed in terms of a covariant gauge derivative which contains the gauge derivative corresponding to minimal coupling, if the universal constantp, characterizing the nonsymmetric theory, is fixed in terms of Planck's constant and the elementary quantum of charge. By this choice the spinor representation of the linear connection becomes closely related to the spinor affinity used by Infeld and Van Der Waerden in their generally covariant formulation of Dirac's equation.     

Already unified field theory with non-covariant geometrization

In general relativity the non-covariant ansatzA ⁱ = ₄ ⁱ for the vectorpotentialA _k gives the general solution of the Maxwell equations as four coordinate conditions which are the conditions of integrability of the Einstein equations. In the some sense the ansatz=X ⁴ is a general solution of the scalar wave-equation in a reference system given by one coordinate-condition. We discuss the meaning of the canonical quantization of the fields in such reference systems.