Maxwell Electrodynamics Research Articles

Nonlinear electrodynamics and FRW cosmology

Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. We show that this singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory. A mathematical toy model is proposed for which the analytical nonsingular extension of FRW solutions is obtained.

Proposed experiment to test photon anticorrelation with quantitatively controllable source emission rate

We describe a proposed experiment that will establish whether or not the optical field is quantized. We argue that previous attempts to establish this have not been conclusive. Quantum optics and Maxwell electrodynamics predict different outcomes for the experiment which is an improved version of that performed by Brown and Twiss in 1956 (Nature 177 27-9). The Brown-Twiss experiment did not distinguish between the two theories because its source was classical. In the proposed experiment, a weak light signal is achieved without selective deletion, and it can be either Poissonian or sub-Poissonian.

Black holes in three-dimensional Einstein-Born-Infeld-dilaton theory

The three-dimensional static and circularly symmetric solution of the Einstein-Born-Infeld-dilaton system is derived. The solutions corresponding to low energy string theory are investigated in detail, which include black hole solutions if the cosmological constant is negative and the mass parameter exceeds a certain critical value. Some differences between the Born-Infeld nonlinear electrodynamics and the Maxwell electrodynamics are revealed.

On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics

Recent experimental results such as those on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schrödinger equations, e.g., as proposed by Doebner and Goldin, yields a consistent, nonlinear, Galilean Schrödinger–Maxwell electrodynamics.

FIELD THEORIES FROM THE RELATIVISTIC LAW OF MOTION

From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which could be the Abelian Maxwell electrodynamics or the non-Abelian Yang–Mills theory. On the other hand, the quadratic law demands space–time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tensor theory of gravitational field — general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.

Observation of dynamical localization in a rough microwave cavity

We measure the angular momentum content of modes in a flat, near-circular microwave cavity with a rough perimeter and demonstrate localization in angular momentum space. Because Schrödinger's wave mechanics and Maxwell's electrodynamics are equivalent for a 2d cavity, we compare our experimental results directly with the quantum theory of rough 2d cavities [K.M. Frahm and D.L. Shepelyansky, Phys. Rev. Lett. 78 (1997) 1440]. Introducing the concept of effective roughness we find good qualitative agreement.

Ludwig Boltzmann. The Man Who Trusted Atoms

Although Boltzmann belongs among the most influential scientists of the 19th and 20th centuries, when physics became the fundamental science describing nature, there does not yet exist a detailed scientific biography. The present book, on first inspection, promises to fill this gap since it covers, besides a 'short biography', the following topics pioneered by Boltzmann: the collision equation, the H-theorem, the statistical interpretation of entropy, equilibrium statistical mechanics, and the theory of polyatomic molecules. Moreover, there is an introduction on physics before Boltzmann, especially on kinetic theory, as well as chapters on his philosophy, his relation to contemporaries and his influence on early 20th-century physicists. A translation of A German professor's journey into Eldorado and several technical appendices complete the volume. In spite of this survey of important topics from Boltzmann's lifework, we hesitate to call this book a balanced biography. Not only are few original sources used to provide a more detailed portrait of the circumstances of his life, or to characterize the various stages of, and especially connections between, his many fields of work, but the selection also depends very much on the author's preferences. Thus Cercignani puts great emphasis on dealing with the collision equation and its development far into the 20th century, whereas he relies more or less on foreign analysis of the remaining topics - which are often covered in a fairly scattered way, such as the work on Maxwell's electrodynamics (which dominated Boltzmann's interest for several years). Also many of his interactions with colleagues, such as Helmholtz and Mach, are quite under-represented. On the other hand, Cercignani's book constitutes a quite serious and welcome biographical sketch on the way towards the really great biography, which this giant of science deserves.

One And The Same Route: Two Outstanding Electrodynamics

We show that the same route that leads to Maxwell's electrodynamics leads also to Podolsky's electrodynamics, provided we start from Podolsky's electrostatic force law instead of the usual Coulomb's law.

Hamiltonian structure for classical electrodynamics of a point particle

We prove that, contrary to the common belief, the classical Maxwell electrodynamics of point-like particle may be formulated as an infinite dimensional Hamiltonian system. We derive a well defined quasi-local Hamiltonian which possesses direct physical interpretation being equal to the total energy of the composed system (field + particle). The phase space of this system is endowed with a very interesting symplectic structure. We prove that this structure is strongly nondegenerate and, therefore, enables one to define the consistent Poisson bracket for the particle and field degrees of freedom. We stress that this formulation is perfectly gauge invariant.

Aux confins de l'électrodynamique maxwellienne : Ions et électrons en 1897/The limits of Maxwellian electrodynamics : Ions and electrons in 1897

SUMMARY. — The concept of the electron was constructed in a gradual and multifarious manner, during the last decade of the 19th century. The present essay links the complexity of this process to the difficulties of a major historical transition : the incorporation of ions into Maxwell's electrodynamics. The transition followed different routes, within strongly individualized experimental and theoretical traditions, corresponding each time to a different ancestor of the electron.

Teleparallel Kähler Calculus for Spacetime

In a recent paper [J. G. Vargas and D. G. Torr, Found. Phys. 27, 599 (1997)], we have shown that a subset of the differential invariants that define teleparallel connections in spacetime generates a teleparallel Kaluza-Klein space (KKS) endowed with a very rich Clifford structure. A canonical Dirac equation hidden in this structure might be uncovered with the help of a teleparallel Kahler calculus in KKS. To bridge the gap to such a calculus from the existing Riemannian Kahler calculus in spacetime, we commence the construction of a teleparallel Kahler calculus in spacetime. In the process, we notice: (a) Unknown to him, one of Einstein's equations in his attempt at unification with teleparallelism states that the interior covariant derivative of the torsion is zero. (b) A mechanism exists in the tangent bundle of teleparallel spaces for producing confinement (in the applicable cases, one would have to show why nonconfinement also occurs, rather than the other way around). (c) When the torsion is not zero, the interior covariant derivative in the sense of Kahler, δF, does not coincide with *d*F. The system (dF = 0, δF = j) rather than (dF = 0, *d*F = j) should then be used for generalizations of Maxwell's electrodynamics.

Energy and momentum for the electromagnetic field described by three outstanding electrodynamics

A prescription for computing the symmetric energy–momentum tensor from the field equations is presented. The method is then used to obtain the total energy and momentum for the electromagnetic field described by Maxwell electrodynamics, Born–Infeld nonlinear electrodynamics, and Podolsky generalized electrodynamics, respectively.

Principles of discrete time mechanics: II. Classical field theory

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrödinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrödinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein - Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantization of discrete time mechanics and discrete time quantum electrodynamics.

Dielectric dispersion of a membrane consisting of a large number of solid bilayers containing mobile ions

The complex permittivity and the impedance of a lamellar membrane consisting of a repetition unit of two conducting dielectrics is calculated using the linearized Nernst–Planck–Maxwell electrodynamics previously developed for isolated interfaces, lamellar films with identical cation and anion mobility inside each type of lamella and with identical Nernst distribution coefficients and for homogeneous polymer films with ionic impurities. Any intrinsic dielectric dispersion of the two (ion-free) dielectrics is neglected and periodic boundary conditions are assumed in a infinite array of identical bilayers. The anion and the cation may be of any charge type and their diffusion coefficients may have any values in the two dielectrics. The Nernst distribution coefficient may be different for the cation and the anion within limits determined by the validity of the linearisation procedure. The calculated complex permittivities of the composite material may differ substantially from the permittivities calculated by a simple Maxwell–Wagner–Sillars (MWS) procedure because of the dynamical electrical double layers formed at 1–2 Debye lengths from the interfaces. These polarisation layers give rise to the so-called excess impedance. The MWS results are, however, always exact in the high-frequency limit. Furthermore, the MWS approach is correct for the dielectric loss at low frequencies. A frequency weighted ‘Cole–Cole plot’ of the real and imaginary components of the excess impedance has a characteristic ‘apple shape’ starting in the origin at very low frequencies and moving clockwise around the origin with increasing frequency. In the high-frequency limit, the origin is always approached in the fourth quadrant along a line with slope-1. The low-frequency asymptote of the frequency weighted Cole–Cole plot for the excess impedance is sensitive to the special conditions, however. The Cole–Cole plots of the total membrane impedance (MWS+excess) exhibit sometimes two partially overlapping semi-circular arcs, one for each type of lamella. When the thickness of the lamellae becomes of the same order of magnitude as the Debye length, the distinction between the two relaxations is wiped out and only a single, flattened arc is seen. A model lamellar ‘cellulose acetate’ (CA) membrane, consisting of alternating layers of ‘wet CA phase’ and ‘aqueous microphase’ with NaCl dissolved, is investigated. The parameters of the membrane are chosen quite realistically (except the one-dimensional geometry) as those pertaining to dense CA membranes, in accordance with previous emf and impedance spectroscopical studies of dense and asymmetric cellulose acetate membranes. The usual electrochemical ‘equivalent circuit’ approach, connecting in parallel the membrane resistance and the membrane capacitance, is put to a test. From the time constant related to the maximum negative reactance the so-called ‘geometric capacitance’ is calculated. From this, the ‘geometric’ membrane permittivity of the membrane is found. At low salt concentrations, the geometric permittivity coincides with the low-frequency limit of the membrane permittivity, but with increasing salt concentrations the geometric permittivity increases less rapidly with concentration than does the low-frequency membrane permittivity. The geometric membrane permittivity seems to be a complicated mean value between the low-frequency membrane permittivity and the high-frequency membrane permittivity (independent of concentration), since the characteristic frequency for the impedance relaxation is many orders of magnitude higher than the characteristic frequency of the dielectric relaxation. The former is related to the diffusional relaxation time of the CA layer, the second to the relaxation time in the aqueous microphase.

Neutral particles with spin 1/2 and action-at-a-distance theory.

The first example of the classical action-at-a-distance theory describing the electromagnetic interactions of neutral particles with spin 1/2 and an anomalous magnetic moment is presented. The fundamental role of supersymmetry in the construction of the presented theory is shown. A generalization to superparticles having an electric charge and an anomalous magnetic moment is considered. A new generalized minimality principle in superspace is revealed for supersymmetric Maxwell electrodynamics, including the electric charge and anomalous magnetic moment of particles with spin 1/2 on equal ground. {copyright} {ital 1996 The American Physical Society.}

Massive Electrodynamics and Magnetic Monopoles

Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist within this theory. Assuming that the space-time is torsionless, taking the photons mass zero, and turning to the Einstein gauge we obtain Maxwell's electrodynamics.

Original Article Extended approaches to covariant Maxwell electrodynamics

Original Article Extended approaches to covariant Maxwell electrodynamics

Extended approaches to covariant Maxwell electrodynamics

The field equations of covariant Maxwell electrodynamics are a set I of 8 equations for the determination of 6 variables, i.e., the independent components of the skew-symmetric Maxwell tensorF αβ . Obviously 2 of these equations are not evolutive; however they cannot be eliminated without losing manifest covariance. This paper presents a new hyperbolic set S of 8 equations in the 8 variablesF αβ ,x, y, wherex, y are new auxiliary quantities. The solutions of S withx =y = 0 are those of the set I. Moreover, S is expressed in covariant form and is equivalent to a symmetric hyperbolic system.

Some Algebraic Properties of Maxwell-Dirac Isomorphism

Abstract A new derivation of the Maxwell-Dirac isomorphism is presented. A complete set of transformations connecting Maxwell's electrodynamics and wave mechanics is obtained.

Classical field theory and analogy between Newton's and Maxwell's equations

A bivertical classical field theory includes the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows one to recognize the formal analogies among Newtonian mechanics and Maxwell's electrodynamics.