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.     

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.     

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.     

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.     

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.     

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.     

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.     

Electromagnetic mass shifts in non-Lagrangian field theory

The electromagnetic interactions of hadrons are considered in a model in which both the hadrons and the photons are spinless. The perturbation theory of this model is developed in a way which takes the strong interactions rigorously into account. An expression for the second-order electromagnetic mass shifts of the hadrons is derived. The customary formula expressing these mass shifts as integrals over the Compton scattering amplitude is shown to be inaccurate. The correct expression differs from the old one by a changed integration contour. In favourable cases the two expressions coincide if the integrations over the four components of the photon momentum are carried out in a certain order. This order of integration must in general not be changed.     

An electrical test particle in Einstein's unified field theory

Previous work on a class of exact solutions to the field equations of Einstein's unified field theory has shown that some of these solutions acquire an immediate physical meaning as soon as one allows for external sources, as it occurs in the general theory of relativity. It is evident that a four-current density j ⁱ , appended to the right-hand side of the field equation , has a fundamental role: in some solutions, a string built with this current density gives rise to partons, mutually interacting with forces that do not depend on distance, like the ones invoked to explain the confinement of quarks. In other solutions, for which obeys Maxwell's equations, jⁱ clearly displays electrical behavior. In the present paper it is shown under what conditions the electrical behavior of a charged test particle can be extracted from the field equations and from conservation identities related to the theory, when sources are appended in the way proposed by Borchsenius and Moffat.     

Five-dimensional unified field theory: The source function

In Kaluza's five-dimensional unified field theory the restriction for the 55 component of the metric tensor ₅₅=1 demands that the 15 equations for the unified field be weakened. Equations which have been proposed have identically vanishing trace. The equations then admit only a radiation field as source of the gravitational field. By relaxing the condition, this limitation is avoided, while retaining the striking successes of the five-dimensional approach. A scalar function, determined by the 15th field equation apart from integration constants, provides source terms for both the gravitational and electromagnetic fields, in the latter case of polarization type.     

On five-dimensional unified field theory and projective relativity

The choice between the Kaluza-Klein and the Jordan-Thiry forms of five-dimensional unified field theory has been considered by McInnes. Here a reply is made to criticisms by McInnes of a previous paper. In addition, the implications of projective relativity are considered.     

An extension of the nonsymmetric unified field theory

The field equations, in the new formulation of Einstein's unified field theory, are extended from the present vacuum form to the general case in which sources are present. In this generalization the contracted torsion tensor corresponds to the electromagnetic four-potential. By this correspondence, Einsteins-gauge transformation becomes identical to the ordinary electromagnetic gauge symmetry. The generalized Bianchi identities are found and used to discuss deviations from the Einstein-Lorentz equations of motion.     

A geometric foundation for a unified field theory

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists an N-dimensional linear vector space with N5. This space is decomposed into a four-dimensional tangent space and an (N - 4)-dimensional internal space. On the basis of geometric considerations, one arrives at a number of fields, the field equations being derived from a variational principle. Among the fields obtained there are the electromagnetic field, Yang-Mills gauge fields, and fields that can be interpreted as describing matter. As a simple example, the case N=6 is considered.     

Classical gravity and quantum matter fields in unified field theory

The Einstein-Schrödinger purely affine field theory of the non-symmetric field provides canonical field equations without constraints. These equations imply the Heisenberg-Pauli commutation rules of quantum field theory. In the Schrödinger gauging of the Einstein field coordinatesU _kl ⁱ = _kl ⁱ – _l ⁱ _km ^m , this unified geometric field theory becomes a model of the coupling between a quantized Maxwellian field in a medium and classical gravity. Therefore, independently of the question as to the physical truth of this model, its analysis performed in the present paper demonstrates that, in the framework of a quantized unified field theory, gravity can appear as a genuinely classical field.     

Electromagnetic mass shift of pions in unified gauge field theories and the light-cone

The electromagnetic mass shift of pions is discussed in unified gauge field theories of weak and electromagnetic interactions to second order of the electric charge and the pion mass, respectively. We calculate the contributions of the next to leading light-cone singularities (quark mass terms) and it is found that these do not contribute to the divergences in the mass shift provided the masses of the bare proton quark and neutron quark are equal. γ, Z, W, φ exchanges are taken into account. Different bare quark masses in general make the mass shift divergent. In the tadpole contribution, the Born term causes a divergence unless we extrapolate first to q² = 0.     

Spinor matter in a particular 5-dimensional projective unified field theory

After presenting the foundation and the basic equations of a new 5-dimensional projective unified field theory, the problem of incorporating spinor fields into this framework is investigated. Apart from Pauli's method, we propose a new approach which leads to a consistent 5-dimensional spinor theory with a series of physical consequences (variability of the 4-dimensional rest mass, instability of 4-dimensional stationary states, etc.).Dedicated to Prof. Peter Bergmann on the occasion of this 70th birthday.     

Toward a unified field theory of gravitation and strong interactions

The chiralSU(3) quark model is shown to be a consequence of general relativity for Petrov type Id space-times, in much the same way that the Dirac equation is a consequence of special relativity.     

A new unified field theory based on the conformal group

We develop here a new unified theory of the electromagnetic and gravitational field, based on a six-dimensional generalization of Maxwell's equations; additional space-time coordinates are interpreted only as mathematical tools in order to obtain a linear realization of the four-dimensional conformal group.