Minimum size of charged particles in general relativity

Spherical charged matter distributions are examined in a coordinate-free manner within the framework of general relativity. Irrespective of models chosen to describe the interior structure of a charged particle, it is found that the latter's total gravitational mass is positive definite, being finite only when there exists a lower bound for its invariant extension. For a simple choice of matter and charge distributions it is then shown that there is a minimum invariant size for the particle, below which no solution of the field equations exists, the matter density becoming negative and the spacetime developing an intrinsic singularity in the exterior of the particle for radii less than this minimum. A mass renormalization is derived, valid at the moment of time symmetry, which relates the particle's total mass to its charge, bare mass and invariant extension. Our results are compared with those obtained previously by Arnowitt, Deser and Misner, who consider the simpler distribution of a charged spherical shell. Qualitatively, the two situations share the same features. However, in the more realistic spherical distributions the formulae are correspondingly more complicated, and the minimum extension is found to be greater than that of the shell, as one might expect on physical grounds. Moreover, the correspondence between negative valued matter distributions and intrinsic singularities was not evident in the shell case.     

Black holes and the classical model of a particle in Einstein non-linear electrodynamics theory

Modified by a logarithmic term, the non-linear electrodynamics (NED) model of the Born–Infeld (BI) action is reconsidered. Unlike the standard BI action, this choice provides interesting integrals of the Einstein-NED equations. It is found that the spherical matching process for a regular black hole entails indispensable surface stresses that vanish only for a specific value of the BI parameter. This solution represents a classical model of an elementary particle whose radius coincides with the horizon. In flat spacetime, a charged particle becomes a conducting shell with a radius proportional to the BI parameter.     

Classical and Quantum Radiation Reaction for Linear Acceleration

We investigate the effect of radiation reaction on the motion of a wave packet of a charged scalar particle linearly accelerated in quantum electrodynamics (QED). We give the details of the calculations for the case where the particle is accelerated by a static potential that were outlined in Higuchi and Martin Phys. Rev. D 70 (2004) 081701(R) and present similar results in the case of a time-dependent but space-independent potential. In particular, we calculate the expectation value of the position of the charged particle after the acceleration, to first-order in the fine structure constant in the ℏ→ 0 limit, and find that the change in the expectation value of the position (the position shift) due to radiation reaction agrees exactly with the result obtained using the Lorentz-Dirac force in classical electrodynamics for both potentials.     

Equivalence Principle and Radiation by a Uniformly Accelerated Charge

We address the old question of whether or not a uniformly accelerated charged particle radiates, and consequently, if weak equivalence principle is violated by electrodynamics. We show that radiation has different meanings; some absolute, some relative. Detecting photons or electromagnetic waves is not absolute, it depends both on the electromagnetic field and on the state of motion of the antenna. An antenna used by a Rindler observer does not detect any radiation from a uniformly accelerated co-moving charged particle. Therefore, a Rindler observer cannot decide whether or not he is in an accelerated lab or in a gravitational field. We also discuss the general case.     

On the Electromagnetic Origin of Inertia and Inertial Mass

We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton’s second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle’s own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle’s vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle’s vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the “4/3 mass paradox” for a spherical charge distribution.     

Dispersion relation of dust acoustic waves in metallic multi-walled carbon nanotubes

In this paper,a charged multi-walled carbon nanotube(MWCNT),which is surrounded by charged nanoparticles,is modeled as a cylindrical shell of electron-ion-dust plasma.By employing classical electrodynamics formulations and the linearized hydrodynamic model,the dispersion relation of the dust acoustic wave oscillations in the composed system is investigated.We obtain a new low-frequency electrostatic excitation in the MWCNT,i.e.dust acoustic wave oscillations.     

Cornelius Lanczos’s Derivation of the Usual Action Integral of Classical Electrodynamics

The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles.     

Thin-Shell Wormholes from Regular Charged Black Holes

We investigate a new thin-shell wormhole constructed by surgically grafting two regular charged black holes arising from the action using nonlinear electrodynamics coupled to general relativity. The stress-energy components within the shell violate the null and weak energy conditions but obey the strong energy condition. Several other aspects of this thin-shell wormhole are also analyzed. The most important finding is that the presence of a charge is essential for producing a thin-shell wormhole that is stable to linearized spherically symmetric perturbations about a static equilibrium solution. The precise conditions depend on various properties of the black hole.     

Inertial mass and the quantum vacuum fields

Even when the Higgs particle is finally detected, it will continue to be a legitimate question to ask whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter. General relativity specifies which geodesic path a free particle will follow, but geometrodynamics has no mechanism for generating a reaction force for deviation from geodesic motion. We discuss a different approach involving the electromagnetic zero‐point field (ZPF) of the quantum vacuum. It has been found that certain asymmetries arise in the ZPF as perceived from an accelerating reference frame. In such a frame the Poynting vector and momentum flux of the ZPF become non‐zero. Scattering of this quantum radiation by the quarks and electrons in matter can result in an acceleration‐dependent reaction force. Both the ordinary and the relativistic forms of Newton's second law, the equation of motion, can be derived from the electrodynamics of such ZPF‐particle interactions. Conjectural arguments are given why this interaction should take place in a resonance at the Compton frequency, and how this could simultaneously provide a physical basis for the de Broglie wavelength of a moving particle. This affords a suggestive perspective on a deep connection between electrodynamics, the origin of inertia and the quantum wave nature of matter.     

Mass generation in finite temperature QED

Quantum electrodynamics at finite temperature is studied from the point of view of mass generation. Using Ueda's definition of the temperature-dependent mass of the particle on its mass shell at zero temperature and the real time formalism, results obtained by earlier workers are rederived in a manifestly gauge invariant fashion. Some cosmological implications of the plasmon effect are discussed.     

Source Methods in Quantum Field Theory

Schwinger's source theory is used to present a pedagogical review of various methods and models in quantum field theory. In the interest of simplicity we start out with a charged scalar model. Later on we also incorporate more complicated concepts in order to treat quantum electrodynamics, effective Lagrangians and model approximations.     

Self-interaction in the Bopp–Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration?

In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp–Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.     

Infrared problem in QED and electric charge renormalization

The electric charge renormalization in quantum electrodynamics is discussed, by taking into account the fact that an “infrared dressing transformation” is needed to go from the local states occurring in the Green's functions, to the (physical) charged states which obey Gauss' law. Apparent difficulties discussed in the literature are resolved. The construction of physical multicharged states is discussed explicitly.     

Stochastic electrodynamics. I. On the stochastic zero-point field

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.     

Quantum analog of Lienard-Wichert potentials

In the framework of quantum electrodynamics the vector potential is computed of the electromagnetic field created by a localized wave packet corresponding to a uniformly moving charged particle. It is shown that the field distribution near the particle trajectory depends on mass renormalization due to the interaction with the transverse quantum field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–70, September, 1990.     

The wave properties of matter and the zeropoint radiation field

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a charged particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc²/. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schrödinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis appled to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation. Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schrödinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated waveand the ensemble of particles.     

A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Charged particle's tunneling radiation from the charged BTZ black hole

An extension of the Parikh–Wilczek's semi-classical quantum tunneling method, the tunneling radiation of the charged particle from a charged BTZ black hole was investigated. Difference from the uncharged mass-less particle, the geodesics of the charged massive particle tunneling from the black hole is not light-like, but determined by the phase velocity. The derived result shows that the tunneling rate depends on the emitted particle's energy and electric charge, and takes the same functional form as uncharged particle. It also prove that the exact emission spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory.