The Relativistic Dynamics of the Combined Particle–Field System in Renormalized Classical Electrodynamics

This paper develops a general theory for the nonlinear, renormalized interaction between charged particles and electromagnetic fields. For the combined “particle + field” system, a fundamental relativistically invariant dynamical equation is derived from first principles. This theory was first obtained in an alternative way by one of us (J.K.) in an earlier paper. Here, we prove that the initial-value problem for the “particle + field” system is well-posed. The existence and uniqueness result is based on a careful analysis of the singularites of the electromagnetic field along the trajectory of the moving charged particle. Furthermore, the Banach fixed-point principle is used. The theory improves the classical Dirac theory for the motion of electrons. In particular, it is shown how to deal with the Dirac paradox of runaway solutions. Received: 10 December 1997 / Accepted: 21 April 1998     

Space-time structure and bound-charge fields

Together with a “postulate of equivalent situations,” the exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) makes it possible to find the space-time structure and fields of charged conductors of arbitrary shape without using the Einstein equations. The energy of the electric field outside of a charged plane, which is equal to the rest energy of the masses of the charges creating the field, is determined. The space-time metric outside of the charged plane is established; it could also have been found from the exact solution of the Einstein-Maxwell equations. This solution describes the equilibrium of charged dust in parallel electric and gravitational fields. The field and metric are found outside of a charged conducting sphere. While it eliminates the self-energy divergence, the proposed method renders the classical electrodynamics internally consistent on transition to any short distance. All-Russian Scientific Research Institute of Opticophysical Measurements. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–74, October, 1997.     

The Origins of the Field Concept in Physics

The term, “field,” made its first appearance in physics as a technical term in the mid-nineteenth century. But the notion of what later came to be called a field had been a long time in gestation. Early discussions of magnetism and of the cause of the ocean tides had long ago suggested the idea of a “zone of influence” surrounding certain bodies. Johannes Kepler's mathematical rendering of the orbital motion of Mars encouraged him to formulate what he called “a true theory of gravity” involving the notion of attraction. Isaac Newton went on to construct an eminently effective dynamics, with attraction as its primary example of force. Was his a field theory? Historians of science disagree. Much depends on whether a theory consistent with the notion of action at a distance ought qualify as a “field” theory. Roger Boscovich and Immanuel Kant later took the Newtonian concept of attraction in new directions. It was left to Michael Faraday to propose the “physical existence” of lines of force and to James Clerk Maxwell to add as criterion the presence of energy as the ontological basis for a full-blown “field theory” of electromagnetic phenomena.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

The Newtonian limit of spacetimes for accelerated particles and black holes

Solutions of vacuum Einstein’s field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor–Swaminarayan solutions, self-accelerating “dipole particles”, and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes. Dedicated to the memory of Jürgen Ehlers (29 December 1929 to 20 May 2008).     

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

“Non-Gibbsian” States and their Gibbs Description

The driving principle behind this paper is the following thesis: “Every physically reasonable random field has to be a Gibbs random field”. In this paper the so-called “non-Gibbsian” random fields are considered. The usual definition of the Gibbs field is generalized in such a way so as to include some of the discovered “non-Gibbsian” fields. The new definition is then used to show that the projection of the two-dimensional Ising model onto the one-dimensional sublattice ℤ¹ falls into the class of the generalized Gibbs fields. Received: 13 March 1998 / Accepted: 19 June 1998     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

Ferromagnetic resonance and bistability field in a uniaxial magnetic film

Peculiarities of ferromagnetic resonance (FMR) corresponding to bias along the “hard” magnetic axis of a film with 2D uniaxial anisotropy are studied based on numerical solution of magnetic moment dynamics equations. It is shown that an additional resonance peak is formed in the FMR spectrum in the vicinity of “bistability field” H _b . The dependence of this field on the amplitude of the microwave field and damping parameters is analyzed.     

Destruction of the long-range antiferromagnetic order by defects of the “random local field” type

The behavior of diluted antiferromagnets in an external magnetic field has been considered. It has been shown that, because the “force” of induced defects of the “random local field” type depends on the magnetic induction, the destruction of the long-range antiferromagnetic order by these defects in space of dimension d ≥ 2 is impossible.     

Shell phenomena in mesoscopic systems: From nuclei to quantum dots

The evolution of shape parameters and giant dipole and octupole resonances in rotating nuclei, the role of main classical orbits for deformed systems with octupole and hexadecapole deformations, the occurence of magic numbers under a perpendicular magnetic field in small quantum dots are discussed from the point of view of the manifestation of shell effects in a finite Fermi system. Presented by R.G. Nazmitdinov at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Rotating superconductors: Ginzburg-Landau equations

Superconductors put into rotation develope a spontaneous internal magnetic field (the “London field”). In this paper Ginzburg Landau equations for order parameter, field, and current distributions for superconductors in rotation are derived. Two simple examples are discussed: the massive cylinder and the “Little and Parks geometry”: a thin film of superconducting material deposited on a cylinder of normal material. A dependence of T _c on rotational frequency is predicted. The magnitude of the effect is estimated and should be observable. Received 28 May 2001     

A twist in the geometry of rotating black holes: seeking the cause of acausality

We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is opposite to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this.     

The electromagnetic energy with the truncation method for a five-dimensional rotating black hole in a uniform magnetic field

We consider a charged five-dimensional Myers–Perry black hole in a uniform magnetic (test) field. Using the Komar mass formula, we calculate the total energy of the electromagnetic field within the truncation three-sphere for a five-dimensional rotating black hole with two equal-rotation parameters and two equal-magnetic field strengths. We show that the total electromagnetic energy takes the minimum value when the five-dimensional rotating black hole acquires a non-zero net electric charge Q.     

Anti-de Sitter quotients,bubbles of nothing,and black holes

In 3+1 dimensions there are anti-de Sitter quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de Sitter solution (and appropriate identifications) one finds two one parameter families of spacetimes that contain these quotient black holes. One of these families consists of B-metrics (“bubbles of nothing”), the other of black hole spacetimes. All of them have vanishing conserved charges. I. Bengtsson was supported by VR.     

Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable the relativistic dynamic equation for systems with an invariant plane becomes a non-linear analytic equation in one complex variable. We obtained explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock hypothesis and using these solutions, we were able to describe the space-time transformations between two uniformly accelerated and rotating systems. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Noninertial Observers in Special Relativity and Clock Synchronization Debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify “absolute simultaneity” as being “Nature's choice of synchronization” are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most “natural” choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most “natural” (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does not need to be resolved in order to resolve Ehrenfest's paradox.     

Features of radiation from a chain of relativistic charged particles rotating about a dielectric ball

The spectral distribution of the intensity of radiation from a chain of 1 N > equidistant relativistic charged particles uniformly rotating about a dielectric ball weakly absorbing radiation, in its equatorial plane is investigated. In the case of a single particle (N = 1) and of a special values of problem parameters (frequency of charge gyration, distance between the charge and the ball surface, dielectric permittivity of the ball material), the radiation at certain harmonics with k ≫ 1 may be more intensive by tens of times than that for a charge uniformly rotating in a continuous and infinite medium (having the same dielectric permittivity as that for the ball material). Numerical results testify that if one replaces a single particle rotating about a ball by a chain of N = mk charges (m = 1;2;3...), then the radiation may be amplified by N ² times due to the constructive interference of electromagnetic waves generated by different charges of the chain. The increase in radiated energy is caused by an additional work of external forces sustaining the uniform rotation of charged particles about a dielectric ball.     

A discrete nonetheless remarkable brick in de Sitter: The “massless minimally coupled field”

Over the last ten years interest in the physics of de Sitter space—time has been growing very fast. Besides the supposed existence of a “de Sitterian period” in inflation theories, the observational evidence of an acceleration of the universe expansion (interpreted as a positive cosmological constant or a “dark energy” or some form of “quintessence”) has triggered a lot of attention in the physics community. A specific de Sitterian field called “massless minimally coupled field” (mmc) plays a fundamental role in inflation models and in the construction of the de Sitterian gravitational field. A covariant quantization of the mmc field, à la Krein—Gupta—Bleuler was proposed in Class. Quantum. Grav. 17, 1415 (2000). In this talk, we will review this construction and explain the relevance of such a field in the construction of a massless spin-2 field in de Sitter space—time.     

Tunneling Radiation of Charged and Magnetized Particles from the Reissner-Nordstr?m-de Sitter Black Holes with Magnetic Charges

We extended the Parikh-Wilczek’s method to calculate the tunneling radiation of charged and magnetized particles from the event horizon and the cosmological horizon of the Reissner-Nordstr?m-de Sitter black hole with magnetic charges. We reconstructed the electromagnetic field tensor and recalculated the Lagrangian of the field corresponding to the source with electric and magnetic charges. By viewing the eclectic and magnetic charges as an equivalent electric charge, we obtained the tunneling rate of the charged and magnetized particles. Our calculation supports the conclusion given by Parikh and Wilczek that the emission spectrum is no longer purely thermal, and the emission process supports the information conservation.