Development of the Evans Wave Equation in the Weak-Field Limit: The Electrogravitic Equation

The Evans wave equation [1-3] is developed in the weak-field limit to give the Poisson equation and an electrogravitic equation expressing the electric field strength E in terms of the acceleration g due to gravity and a fundamental scalar potential ⁽⁰⁾ with the units of volts (joules per coulomb). The electrogravitic equation shows that an electric field strength can be obtained from the acceleration due to gravity, which in general relativity is non-Euclidean spacetime. Therefore an electric field strength can be obtained, in theory, from scalar curvature R. This inference is supported by recent experimental data from the patented motionless electromagnetic generator [5].     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.     

Scalar particle with polarizability in a uniform external magnetic field

The model of a scalar structured particle is considered, which possesses polarizability in an external electromagnetic field. The expression for the 4-dimensional current density is found. The exact solution of the equations describing a scalar particle with polarizability in a uniform external magnetic field is obtained. Up to the terms of order O(H²), the energy spectrum can be formally obtained by the substitution of the particle mass in the expression for a pointlike scalar particle: mm–H²/2, where is the magnetic polarizability of the particle. It is shown that the rms radius of a trajectory can be obtained by the substitution of the charge in the well-known formula for a structureless scalar particle: ee(1{-H²/m)^1/2 (where is the electric polarizability).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–94, January, 1991.I thank A. I. L'vov for discussions.     

Nonlinear approach to electrodynamics

A nonlinear approach to electrodynamics is reviewed. On imposing a nonlinear constraintA A = – ², together with the usual gauge-invariant electromagnetic field Lagrangian, it is found that the resulting equations of motion have, besides the photon, a static spherically symmetric extended solution which may be regarded as a charged particle. A magnetic dipole moment (spin) can also arise as a solution of the equations of motion if, as expected, it is treated as a first-order quantum effect. In the limit for small quantum fields and pointlike charged particles, the quantum mechanical equivalence of the approach with the usual Lagrangian formulation of the electromagnetic interaction of a charged scalar field is heuristically shown. Moreover the possibility of constructing charged fermion fields from the solution having both a charge and a magnetic moment is illustrated. In such an approach the photon is associated with the spontaneous breaking of Lorentz symmetry, and the emission of soft photons does not exhibit any infrared divergences.     

A generalized Milne solution for the correlation effects of multiple light scattering with polarization

The Wiener-Hopf method is used to obtain a generalized Milne solution for scalar and electromagnetic fields with single-scattering anisotropy. For the scalar field, the solution found for the time correlation function and the interference component of backscattering is in good agreement with available experimental data. A solution of the Milne problem is constructed for the electromagnetic field. Given anisotropy, the generalized Milne equation is solved in the P₁ approximation for the quantity that describes the degree of depolarization of the scattered light. It is shown that the depolarization of the scattered light can change sign at large anisotropies.     

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find interference effects between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing mass without mass and charge without charge. We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh _v =g _v –n _v . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the gravitational constant). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.     

Electromagnetic Properties of Diquarks

Diquark correlations play an important role in hadron physics. The properties of diquarks can be obtained from the corresponding bound-state equation. Using a model for the effective quark-quark interaction that has been proved successfully in the light meson sector, we solve the scalar diquark Bethe-Salpeter equations and use the obtained Bethe-Salpeter amplitudes to compute the diquarks electromagnetic form factors. The scalar ud diquark charge radius is about 8% larger than the pion charge radius, indicating that these diquarks are somewhat larger in size than the corresponding mesons. We also provide analytic fits for the form factor over a moderate range in Q², which may be useful, for example, in building quark-diquark models of nucleons.     

Derivation of O(3) Electrodynamics from the Irreducible Representations of the Einstein Group

By considering the irreducible representations of the Einstein group (the Lie group of general relativity), Sachs [1] has shown that the electromagnetic field tensor can be developed in terms of a metric q , which is a set of four quaternion-valued components of four-vector. Using this method, it is shown that the electromagnetic field vanishes [1] in flat spacetime, and that electromagnetism in general is a non-Abelian field theory. In this paper the non-Abelian component of the field tensor is developed to show the presence of the B ⁽³⁾ field of the O(3) electrodynamics, and the basic structure of O(3) electrodynamics is shown to be a sub-structure of general relativity as developed by Sachs. The extensive empirical evidence for both theories is summarized.     

Symmetries and the Einstein-Maxwell field equations the null field case

This paper deals with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. The electromagnetic field is assumed to be null. It is proved that if the space-time admits a group of isometrics then the fluid velocityu ⁱ, energy density, pressurep, and charge density are invariant under the group. In addition, if the charge density is nonzero, the electromagnetic field tensorf _ij is also invariant. On the other hand, examples of exact solutions are given which establish that if = 0, thenF _ij is not necessarily invariant under the group. In the case of spherically symmetric space-times, however, in which the group of isometries acting isSO (3),f _ij is invariant, independently of whether or not is nonzero. This result leads to the conclusion that in a spherically symmetric space-time the field equations in question admit no solutions with non-trivial null electromagnetic field.     

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

The unified field theory,combining Kaluza's five-dimensional and Weyl's conformal theories

A version of the five-dimensional unified theory of gravitation, electromagnetism, and scalar field is developed. It is shown that in this theory the main features of Kaluza's five-dimensional theory and the Weyl one, based on non-Riemannian geometry and on conformal mapping, are combined. Some reasons are pointed out for choosing the physical 4-metric to be conformal (with the factor ²=–G ₅₅) to the 4-metric obtained by 1+4 splitting of the initial five-dimensional manifold. It is shown that the electrical charge and current appear in the geometrical theory if the condition of cylindrical symmetry in the fifth coordinate is substituted by the condition of quasicylindrical symmetry (i.e., the physical 4-metric and the vector potential of electromagnetic field remain independent of the fifth coordinate, while the scalar field depends on it). Two kinds of the most important exact solutions of the 15 field equations are considered. They are (1) static spherically symmetrical solutions and (2) homogeneous isotropic cosmological models.     

The Investigation of the Model of Gravitational Repulsion in Einstein's General Theory of Relativity

The gravitational field of a static, sphericallysymmetric source of mass M and scalar charge q isconsidered. It is shown that the metric expression forthis source is considerably simplified in two limiting cases: a) for M2 4q²/G,that is when the mass of the source is the maincontributor in the gravitational field; b) forq² M²G/4, when theenergy-momentum tensor of the static, spherically symmetric scalar field is the main contributorin the gravitational field. In the limiting caseq² M²G/4, the geodesicsof the massive and massless particles are studied. It isshown that gravitational forces of repulsion act on a particle movingnon-radially in this field. As a result, voids should becreated in the region surrounding such sources in theUniverse. Moreover, the stars with considerable scalar charge q² M²G/4 will act not as convexgravitational lenses as in the case whenq² M²G/4, but as concavegravitational lenses for the electromagnetic rays oflarge impact parameter.     

Quantum theory of particles with spin zero and one half in external fields

The unitary (pseudo unitary) time-evolution operator for a particle with spin half (zero) in an external time-dependent electromagnetic (scalar) field is used to generate a Bogoliubov automorphism on the algebra of the free in field. For the case of an electric external field (scalar field) a finite expression for _out is given and theS-matrix constructed. The latter is unitary and implements the Bogoliubov automorphism. Theorems by Shale and Stinespring are rederived.Supported in part by the U.S. Atomic Energy Commission under Contract No. AT-30-1-3829.     

All static and electrically charged solutions with Einstein base manifold in the arbitrary-dimensional Einstein–Maxwell system with a massless scalar field

We present a simple and complete classification of static solutions in the Einstein–Maxwell system with a massless scalar field in arbitrary \(n(\ge 3)\) dimensions. We consider spacetimes which correspond to a warped product \(M^2 \times K^{n-2}\), where \(K^{n-2}\) is a \((n-2)\)-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant real scalar field consists of nine solutions for \(n\ge 4\) and three solutions for \(n=3\). A complete geometric analysis of the solutions is presented and the global mass and electric charge are determined for asymptotically flat configurations. There are two remarkable features for the solutions with \(n\ge 4\): (i) Unlike the case with a vanishing electromagnetic field or constant scalar field, asymptotically flat solution is not unique, and (ii) The solutions can asymptotically approach the Bertotti–Robinson spacetime depending on the integrations constants. In accordance with the no-hair theorem, none of the solutions are endowed of a Killing horizon.     

Plane-Symmetric Solitons of Spinor and Scalar Fields

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S= and P=i⁵; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant = _,^,, that becomes linear at 0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.     

Geometric interpretation of the tensor of an electromagnetic field with orthogonal components E and B

An electromagnetic field with (B, E) = 0 is interpreted geometrically as associating with each point (x, y, z, t) of the projective line ?³. For this field, the general solution to the first four Maxwell equations, ?\(\mathfrak{o}\mathfrak{t}\) F = 0, is obtained. The remaining four equations are reduced, in a field with no charges and currents, to a problem which is bound up with the scalar wave equation.     

The Biot-Savart-Ampère law and the vacuum fieldB (3)

It is shown that the longitudinal vacuum fieldB ⁽³⁾ emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB ⁽³⁾ is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB ⁽³⁾ identifies the quantized photon momentum appearing in the Dirac equation witheA ⁽⁰⁾, wheree is the charge on the electron andA ⁽⁰⁾ the amplitude of the vector potential. The condition =eA ⁽⁰⁾ can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field.     

Conformal invariance and torsion in general relativity

We study a theory for gravity in which the linear connections are assumed to be arbitrary, except that they are restricted to satisfy the metric condition g =0. A scalar field is added to the theory, and a conformally invariant action integral, linear in the curvature tensor, is defined. The linear connections emerging from the variational principle contain torsion that is related to a propagating spin-1 vector field, identified as the electromagnetic gauge potential. We obtain a set of conformally invariant equations for the metric field, and conclude that Einstein's equations arise from a particular choice of gauge. Finally, spin-1/2 fields are introduced by means of the vierbein formalism, and the qualitative features of the theory are maintained.     

Self-Similar Static Spherically Symmetric Scalar Field Models

Dynamical systems techniques are used to study the class of self-similar static spherically symmetric models with two non-interacting scalar fields with exponential potentials. The global dynamics depends on the scalar self-interaction potential parameters k ₁ and k ₂. For all values of k ₁, k ₂, there always exists (a subset of) expanding massless scalar field models that are early-time attractors and (a subset of) contracting massless scalar field models that are late-time attractors. When k ₁ 1/ and k ₂ 1/ , in general the solutions evolve from an expanding massless scalar fields model and then recollapse to a contracting massless scalar fields model. When k ₁ < 1/ or k ₂ < 1/ , the solutions generically evolve away from an expanding massless scalar fields model or an expanding single scalar field model and thereafter asymptote towards a contracting massless scalar fields model or a contracting single scalar field model. It is interesting that in this case a single scalar field model can represent the early-time or late-time asymptotic dynamical state of the models. The dynamics in the physical invariant set which constitutes a part of the boundary of the five-dimensional timelike self-similar physical region are discussed in more detail.