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.     

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.     

Dual geometric field theory

A Weyl geometry with a gauge-invariant, Riemannian subgeometry is used to geometrize the combined Einstein-Maxwell theory. A generalized Hamilton-Jacobi equation from particle mechanics emerges as an immediate consistency requirement. The time-independent, Coulomb field case is found to include at least lowest-order quantum effects as in wave mechanics. Possible microscopic entropy is identified.Work performed under the auspices of the U.S. Department of Energy.     

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.     

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.     

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.     

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.     

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).     

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.     

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.     

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.     

From geometric quantization to conformal field theory

Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant)r-matrices and this geometrical approach.     

Constrained systems: A unified geometric approach

A general geometric framework is devised in order to contain the presymplectic and Lagrangian formalisms as particular cases. We call these objectsconstrained dynamical systems, since their dynamics usually lead toconstraints. Their most elementary properties are studied, and several related structures, especially morphisms, are defined. In particular, a stabilization algorithm is performed. As a byproduct, the dynamics and constraints of the Lagrangian formalism (with the second-order condition) are intrinsically obtained.     

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.     

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.     

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 generalization of field theory to manifolds of arbitrary dimension

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for , while leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as .Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model. Received: 15 October 1998 / Accepted: 4 November 1998