On the entropy of radiation reaction

The inexorable development of ever more powerful laser systems has re-ignited interest in electromagnetic radiation reaction and its significance for the collective behavior of charged matter interacting with intense electromagnetic fields. The classical radiation reaction force on a point electron is non-conservative, and this has led some authors to question the validity of methods used to model ultra-intense laser–matter interactions including radiation reaction. We explain why such concern is unwarranted.     

也谈带电粒子在电磁场中动态受力平衡条件

电磁场中相对论带电粒子的经典轨道运动受到洛伦兹力和辐射阻尼力的影响,在一定条件下会达到受力平衡状态．基于洛伦兹一狄拉克方程,本文介绍了计及辐射阻尼力后电磁场中带电单粒子(包括导体中的自由电子)受力平衡条件的一种可能的相对论协变形式．     

Cross-Term Conservation Relationships for Electromagnetic Energy, Linear Momentum, and Angular Momentum

Cross-term conservation relationships for electromagnetic energy, linear momentum, and angular momentum are derived and discussed here. When two or more sources of electromagnetic fields are present, these relationships connect the cross terms that appear in the traditional expressions for the electromagnetic (1) energy, (2) linear momentum, and (3) angular momentum, over to, respectively, (1) the sum of the rates of work, (2) the sum of the forces, and (3) the sum of the torques, that are due to the fields of each charge or current source acting upon the other charge and current sources. These relationships, although not new, appear to be rarely recognized and used in the physics literature. As shown here, they can be extremely helpful for solving and gaining a deeper physical understanding into a rather diverse range of interesting problems in electrodynamics, including (1) aspects of Poynting's theorem when applied to charged point particles, (2) the detailed physical basis of electrostatic analysis, (3) understanding the connection between different techniques used in the past for solving Casimir force problems, and (4) reconciling the invalidity of Newton's third law in electrodynamics.     

On the theory of diffraction radiation

A macroscopic theory of diffraction radiation emerging when a charged point particle moves in the vicinity of a perfectly conducting screen is developed. The integral equations derived for radiation fields form the basis for analyzing the similarity and difference of diffraction of electromagnetic radiation and diffraction radiation from a charged particle. It is shown that in the case considered here, the widely used model in which the radiation field can be represented as the field of surface current has more stringent limits of application as compared to the classical theory of diffraction. This considerably restricts the applicability of the results obtained earlier using the double-layer method to only ultrarelativistic energies and to transit angles of particles close to the direction of the normal to the screen surface. The method developed here is used for analyzing familiar problems of diffraction radiation, such as radiation emerging during normal transit of a particle along the axis of a circular aperture in the screen, radiation emitted during oblique transit near a perfectly conducting half-plane, and radiation emitted during oblique transit of a particle through a rectangular slit in an infinitely large screen. In the latter case, the results obtained after the limiting transition to zero width of the slit completely coincide with the theory of transition radiation for arbitrary energies of the particle and its angle of incidence to the screen.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.     

A time-symmetric classical electrodynamics

In this theory, both the advanced and retarded Liénard-Wiechert potentials are used to compute the fields of a charged point particle. The incoming radiation from the advanced fields balances the outgoing radiation of the retarded fields, and we assume that there are no radiation reaction terms in the equations of motion of the particles. We further assume that only retarded fields act on particles through the Lorentz force, and that advanced fields act on antiparticles. This is a theory that is symmetric under time reflection (reversal of the direction of motion plus charge conjugation).     

Necessity of acceleration‐induced nonlocality

The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. This locality postulate is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties in general cannot be measured instantaneously. The problem is corrected in nonlocal relativity by supplementing the locality postulate with a certain average over the past world line of the observer.     

Considerations on a unified field theory

A geometrical formulation of gravitational and electromagnetic fields is presented for systems composed of point mass charged particles where the charge is small enough that electromagnetic radiation may be neglected. It is assumed that such charges produce a non-negligible contribution to the metric, and that their motion describes geodesics in the total metric which consists of that due to the charge itself and that due to the external environment of the charge. The above, together with several other assumptions yields the customary Einstein-Maxwell relations. It is demonstrated that this construction is not merely a re-statement of the Einstein-Maxwell theory in different terms.     

Particle Creation in the Effective Action Method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.     

Many-times formalism and Coulomb interaction

We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.     

Radiation Reaction of the Classical Off-Shell Relativistic Charged Particle

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.     

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     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

Analysis of FEL radiation in pulsed raman regime

Summary A direct numerical analysis, based on the Lienard-Wiechert potentials, is performed in the present paper, aiming to describe the relativistic interaction of the electrons composing a high-intensity beam (in Raman regime) both with each other and with the fields of an FEL structure and of an external resonant travelling electromagnetic wave. The different accelerations, due to the various forces acting on the charged particles, are seen to give different contributions to the total radiation field, which are separately considered here. The angular and frequency distributions of the obtained radiation are compared with the analytic ones deduced in the particular case of a single charge launched along the FEL structure. The interference effect between the fields of many bunches is seen to cause the shrinkage of the resulting radiation beam.     

Classical radiation reaction off-shell corrections to the covariant Lorentz force

We show that the problem of radiation reaction may be formulated in a space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0,1,2,3 components correspond to the Maxwell fields). The particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five-dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous nonlinear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that the mass-shell deviation is bounded when the external field is removed.     

Shielding from cosmic radiation for interplanetary missions: Active and passive methods

Shielding is arguably the main countermeasure for the exposure to cosmic radiation during interplanetary exploratory missions. However, shielding of cosmic rays, both of galactic or solar origin, is problematic, because of the high energy of the charged particles involved and the nuclear fragmentation occurring in shielding materials. Although computer codes can predict the shield performance in space, there is a lack of biological and physical measurements to benchmark the codes. An attractive alternative to passive, bulk material shielding is the use of electromagnetic fields to deflect the charged particles from the spacecraft target. Active shielding concepts based on electrostatic fields, plasma, or magnetic fields have been proposed in the past years, and should be revised based on recent technological improvements. To address these issues, the European Space Agency (ESA) established a Topical Team (TT) in 2002 including European experts in the field of space radiation shielding and superconducting magnets. The TT identified a number of open research questions to be addressed, including development and testing of novel shielding materials, studies on the angular distributions of energetic solar particles, and cooling systems for magnetic lenses in space. A detailed report to the ESA will be published within a few months. A summary of the TT conclusions and recommendations will be discussed in this paper, with emphasis on active shielding using superconducting magnets.     

The anomalous radiation force of light on a left-handed material

This paper derives the force of the electromagnetic radiation on left-handed materials (LHMs) by a direct applica-tion of the Lorentz law of classical electrodynamics.The expressions of radiation force are given for TE-polarised and TM-polarised fields.The numerical results demonstrate that electromagnetic waves exert an inverse lateral radiation force on each edge of the beams,that is,the lateral pressure is expansive for TE-polarised beams and compressive for TM-polarised beams.The investigation of the radiation force will provide insights into the fundamental properties of LHMs and will provide to better understanding of the interaction of light with LHMs.     

Critical assessment of the Schrödinger picture of quantum mechanics

We provide an example in which the Heisenberg and the Schrödinger pictures of quantum mechanics give different results, thus confirming the statement of P.A.M. Dirac that the two pictures may lead to inequivalent results. We consider a one-dimensional nonrelativistic charged harmonic oscillator (frequency ω₀ and mass m), and take into account the action of the radiation reaction and the vacuum electromagnetic forces on the charged oscillator. We show that the Heisenberg picture gives the correct value, ℏω₀/2, for the ground state energy of the harmonic oscillator in both cases of classical and quantized vacuum fields. In the case of the Schrödinger picture, considering classical vacuum fields, and using a simple calculation for the classical radiation reaction force that is valid in the limit of large mass (mc²⪢ℏω₀), we obtain the value ℏω₀ for the ground state energy of the harmonic oscillator. We show that the vacuum electromagnetic forces play a very important role in the understanding of this discrepancy.