Original Field Equations Research Articles

Asymptotic ray theory for transient diffusive electromagnetic fields

We develop an asymptotic ray theory for transient diffusive electromagnetic fields in isotropic media. The formulation is first derived in the time Laplace transform domain by introducing an ansatz procedure, whereby appropriate expansions for the electric and the magnetic field strengths are substituted in the original field equations. We arrive at consistent recurrence formulas for the sequences of field amplitude vectors that multiply appropriately chosen asymptotic sequences of algebraic powers of the Laplace transform parameter. These representations differ for the two types of fields (electric and magnetic fields) and for the two types of sources (electric current source and magnetic current source). The exponential part of the field expressions contains the diffusive equivalent of the eikonal function in the asymptotic ray theory of wave propagation. This function satisfies the diffusive equivalent of the eikonal equation. Next, we derive the transport equations for the vectorial electric and magnetic field amplitudes of the successive orders. Transient field representations within the asymptotic ray approximation are then obtained by carrying out the inverse Laplace transformation to the time domain by inspection. The ray approximation thus obtained is asymptotic for “early times”. We consider as an example the case of the electric and the magnetic dipole radiation in a homogeneous medium. Here an exact solution exists, which we show to exhibit the structure of the original ansatz but with a finite number of terms. The asymptotic ray theory for transient diffusive electromagnetic fields is expected to lend itself to important applications in surface, surface‐to‐borehole, and crosswell transient electromagnetic prospecting.

Wormhole cosmic strings.

We construct regular multi-wormhole solutions to a gravitating $\sigma$ model in three space-time dimensions, and extend these solutions to cylindrical traversable wormholes in four and five dimensions. We then discuss the possibility of identifying wormhole mouths in pairs to give rise to Wheeler wormholes. Such an identification is consistent with the original field equations only in the absence of the $\sigma$-model source, but with possible naked cosmic string sources. The resulting Wheeler wormhole space-times are flat outside the sources and may be asymptotically Minkowskian.

Novel quantization phenomenon for relativistic wave equations.

An unexpected phenomenon is shown to arise in the theory of relativistic wave equations. We study the canonical quantization of the Oppenheimer equations with standard creation and annihilation operators. The quantized fields satisfy the original relativistic field equations. Surprisingly, however, in the quantized theory relativistic invariance breaks down completely. Indeed, the two-point function is not relativistically invariant and there is no unitary representation of the Lorentz group.

Infinitesimal Bäcklund transformations and Kac–Moody algebras in general relativity

Infinitesimal Bäcklund transformations are found for the problem of classical general relativity in d dimensions, which by dimensional reduction may be interpreted as gravitation interacting with several Maxwell and scalar fields. The transformations are constructed in terms of the solution of a linear system whose integrability condition yields the original field equations. The Kac–Moody algebra, which generates those transformations, is analyzed.

On a surface integral representation for homogeneous anisotropic regions: two-dimensional case

A mathematical statement of the Huygen's principle for an electromagnetic field in an anisotropic region is obtained by a linear mapping of the original anisotropic region into a complex isotropic region using the material permeability and permittivity tensors. The original field equations are reduced to canonical form so that they resemble Helmholtz equations in transform space. This allows the use Huygen's principle in the transform space, after which the result is mapped back into real space; here the resulting contour quantities can be expressed in terms of tangential field quantities, using Maxwell's equations. The field representation is found to be polarization-dependent. In this two-dimensional analysis, each polarization has a different representation and is therefore treated both separately and using duality. Some elementary applications to scattering are presented and discussed in detail.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Composite Gluons and Effective Nonabelian Gluon Dynamics in a Unified Spinor-Isospinor Preon Field Model

The model is defined by a selfregularizing nonlinear preon field equation and all observable (elementary and non-elementary) particles are assumed to be bound (quantum) states of the fermionic preon fields. In particular electroweak gauge bosons are two-particle composites, leptons and quarks are three-particle composites, and gluons are six-particle composites. Electroweak gauge bosons, leptons and quarks and their effective interactions etc. were studied in preceding papers. In this paper gluons and their effective dynamics are discussed. Due to the complications of a six-particle bound state dynamics the formation of gluons is performed in two steps: First the effective dynamics of three-particle composites (quarks) is derived, and secondly gluons are fusioned from two quarks respectively. The resulting effective gluon dynamics is a non-abelian SU(3) dynamics, i.e. this local gauge dynamics is produced by the properties of the composites and need not be introduced in the original preon field equation. Mathematically these results are achieved by the application of functional quantum theory to the model under consideration and subsequent evaluation of weak mapping procedures, both introduced in preceding papers. PACS 11.10 Field theory. PACS 12.10 Unified field theories and models. PACS 12.35 Composite models of particles.

On conformally covariant spin-2 and spin-3/2equations

The standard massless spin-2 and spin-3/2 equations are not conformally covariant. By varying the coefficients of various terms in these equations the authors derive conformally covariant equations. These equations are then used to construct consistent coupling terms in the original field equations representing the self-interaction and the interaction of massless spin-2 (or 3/2) field with matter.

Classical dynamics in the large N limit

We consider some new techniques for generating the 1/N expansion and point out the possibility that the large N limit can be directly given in terms of some particular real-time classical solutions of the original field equations.

New variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion

A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to viscous fluid mixtures with coupled thermomolecular diffusion. Original dynamical field equations are obtained directly from the variational principle. The use of new fundamental concepts and methods in the thermodynamics of open systems avoids the difficulties inherent in the classical Gibbs approach.The dissipative forces incorporated explicitly in the field equations are expressed by means of a dissipation invariant evaluated in detail in terms of coupled viscous and diffusive properties. Partial pressures and dissipative stresses are given new, unambiguous thermodynamic definitions. Lagrangian type equations with generalized coordinates are also obtained directly from the variational principle. They provide a powerful tool of simplified analysis of complex open systems as well as the foundation of a variety of finite element methods.

The recent renaissance of observational cosmology

It was just 51 years ago, in 1917, that Einstein inaugurated relativistic cosmology in the famous paper which introduced the finite but unbounded universe which is now named after him. Curiously enough this was a false start because the Einstein universe is static, self gravitation being overcome by the repulsive effect of the rather artificial cosmological term which Einstein added to his original field equations of 1915.

Unitarity and causality in a renormalizable field theory with unstable particles

The problems of unitarity, causality and renormalizability are treated in a field theory containing an unstable particle. Perturbation theory is suitably modified and leads to an implicit equation for complete propagators. The S-matrix constructed with these propagators and connecting stable particle states only is shown to be unitary, renormalizable and causal. It is also shown to give rise to interpolating Heisenberg fields which verify the original field equations.

Generalized linear electrodynamics I

A generalized version ofPodolsky’s theory of higher order of the electromagnetic field is dealt with. The original field equations of higher order ofPodolsky’s theory is deduced from a new Lagrangian and the canonical formalism of the field, as well as the laws of conservation in the classical case are investigated.

The relativistic self-consistent field

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.