We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the pre-acceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the terms of self-rotation. The analysis of this eq. shows that on one hand, there is no "runaway" solutions, peculiar to the Lorentz-Dirac eq. of radiating point particle, on the other hand, there appear new problems, among them is the nonexistence of solution for some external moments of force.
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as expected on physical grounds. The relativistic generalization is also presented.
We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric charge is order $R^2$ rather than order $R$ in any physical model, as widely claimed in the literature. This scaling arises as a consequence of Poincaré and gauge symmetries, which can be shown to exclude linear corrections. We use the formalism to calculate the leading order finite size correction to the Abraham-Lorentz-Dirac force.
The region very close to an electron ($r << r_0 = e^2/mc^2 \approx 2.8\times 10^{-13}$ cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account of this well-established physical reality, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics. Such a model enables a consistent picture of classical point charges with finite electromagnetic self-energy. It is further conjectured that the reaction of a point charge to its own electromagneti…
On the model of moving rigid charged body is shown that the Lorentz-Dirac approach to radiation reaction in classical electrodynamics does not work for trajectories of body close to the light cone.
Non-linear electrodynamics arising in the frames of field theories in non-commutative space-time is examined on the base of the Riemann-Silberstein-Majorana-Oppenheimer formalism. The problem of form-invariance of the non-linear constitutive relations governed by six non-commutative parameters θ_{kl} \sim {\bf K} = {\bf n} + i {\bf m} is explored in detail on the base of the complex orthogonal group theory SO(3.C). Two Abelian 2-parametric small groups, isomorphic to each other in abstract sense, and leaving unchangeable the extended constitutive relations at arbitrary six parameters θ_{kl} of…
On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radiation is "very satisfactory".
We consider a self-action problem for an electric charge arbitrarily moving in flat spacetime of three dimensions. Its electromagnetic field satisfies the Maxwell equations in Minkowski space of three dimensions. In this space electromagnetic waves propagate not just at a speed of light, but also at all speeds smaller than or equal to the speed of light. The massive particle may "fill" its own field, which acts on it just like an external one. The radiation reaction is determined by Lorentz force of point-like charge acting upon itself plus non-local term which provides finiteness of the self-…
Using the canonical formalism, Compagno and Persico [J. Phys. A: Math. Gen. 35 (2002) 3629--45] have calculated the 'radiation-reaction' force on a uniform spherical charge moving rigidly, slowly and slightly from its position at the time when the transverse electric field is assumed to vanish. This force is shown to result in the same time-averaged self-force as that which has been obtained by different means for the test charge of a Bohr--Rosenfeld field-measurement procedure and which Compagno and Persico claimed to be incorrect.
A self-action problem for a pointlike charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from the source which then undergoes a radiation reaction. We decompose Noether quantities carried by electromagnetic field into bound and radiative components. The bound terms are absorbed by individual particle's characteristics within the renormalization procedure. Radiative terms together with already renormalized 3-momentum and angular momentum of pointlike…
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved numerically.
Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent $c$-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radia…
A self-action problem for a point-like charged particle arbitrarily moving in flat space-time of six dimensions is considered. A consistent regularization procedure is proposed which relies on energy-momentum and angular momentum balance equations. Structure of the angular momentum tensor carried by the retarded "Liénard-Wiechert" field testifies that a point-like source in six dimensions possesses an internal angular momentum. Its magnitude is proportional to the square of acceleration. It is the so-called {\em rigid} relativistic particle; its motion is determinated by the higher-derivative …
The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincaré invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In particular, almost all solutions are dynamically unstable, and therefore, highly questionable. The question remains whether better equations of motion than LAD can be found to describe the dynamics of charges in the electromagnetic fields. In this paper we present an approach to derive such equations of motions, taking as input the Maxwell equations and a particular …
It is shown that the well-known disparity in classical electrodynamics between the power radiated in electromagnetic fields and the power-loss, as calculated from the radiation reaction on a charge undergoing a non-uniform motion, is successfully resolved when a proper distinction is made between quantities expressed in terms of a "real time" and those expressed in terms of a retarded time. It is shown that the expression for the real-time radiative power loss from a charged particle is somewhat different from the familiar Larmor's formula, or in a relativistic case, from Liénard's formula.
Up until now, a consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The well-known problem is that the standard Lorentz force alone (in the case of point particles) does not lead to a theory in which momentum and energy are conserved. The need of radiation reaction force (or self-force) thus arises. The well known candidate for such force, the Lorentz-Abraham-Dirac reaction force, gives non-causal particle behavior, i.e., the particle starts to move before the arrival of external electromagnetic fields. Alternative, c…
Radiation-Reaction on the Straight-Line Motion of a Point Charge accelerated by a constant applied Electric Field in an Electromagnetic Bopp-Landé-Thomas-Podolsky vacuum
Lancaster University（兰卡斯特大学）；Rutgers, The State University of New Jersey（新泽西州立罗格斯大学）
A fundamental issue in classical electrodynamics is represented by the search of the exact equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field - the so-called radiation-reaction equation of motion (RR equation). In the past, several attempts have been made assuming that the particle electric charge is localized point-wise (point-charge). These involve the search of possible so-called "regularization" approaches able to deal with the intrinsic divergences characterizing point-particle descriptions in classical electrodynamics. In this pape…
We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for…
Studies of the classical theory of charged particles and their radiation initiated by Lorentz and Abraham have attracted our attention over a century. Nevertheless, the correct equation to describe the motion of a point charged particle is still a matter of controversy. And what about a charge "living" inside Flatland, a hypothetical world of two spatial dimensions? What is the equation of motion of a point charge in six dimensions? This book provides a self-contained and systematic introduction to problems of radiation and radiation reaction in classical field theory. Besides conventional ele…
Can the wavelength of a classical electromagnetic field be arbitrarily small, or its electric field strength be arbitrarily large? If we require that the radiation-reaction force on a charged particle in response to an applied field be smaller than the Lorentz force we find limits on the classical electromagnetic field that herald the need for a better theory, i.e., one in better accord with experiment. The classical limitations find ready interpretation in quantum electrodynamics. The examples of Compton scattering and the QED critical field strength are discussed. It is still open to conject…
We derive radiation reaction from QED in a strong background field. We identify, in general, the diagrams and processes contributing to recoil effects in the average momentum of a scattered electron, using perturbation theory in the Furry picture: we work to lowest nontrivial order in the electromagnetic coupling alpha. For the explicit example of scattering in a plane wave background, we compare QED with classical electrodynamics in the limit h-bar goes to zero, finding agreement with the Lorentz-Abraham-Dirac and Landau-Lifshitz equations, and with Larmor's formula. The first quantum correct…
The emission from an electron in the field of a relativistically strong laser pulse is analyzed. At the pulse intensities of \ge 10^{22} W/cm^2 the emission from counter-propagating electrons is modified by the effects of Quantum ElectroDynamics (QED), as long as the electron energy is sufficiently high: E \ge 1 GeV. The radiation force experienced by an electron is for the first time derived from the QED principles and its applicability range is extended towards the QED-strong fields.
A study of the radiation-reaction on a point charge that moves along a constant applied electric field in an electromagnetic Bopp-Landé-Thomas-Podolsky vacuum
When accelerated by a constant force in the lab frame, a classical charge experiences no self force. In this case, the particle radiates without dissipating its kinetic and potential energy. But what happens when the particle enters another region with equal and opposite acceleration? Does the oscillating charge lose its mechanical energy similar to a radiating dipole, even though it seems to lose no mechanical energy within each region of constant acceleration? In this paper, I will show how mechanical energy is transferred to radiation energy via the Schott energy when the particle crosses t…
PyCharge is a computational electrodynamics Python simulator that can calculate the electromagnetic fields and potentials generated by moving point charges and can self-consistently simulate dipoles modeled as Lorentz oscillators. To calculate the total fields and potentials along a discretized spatial grid at a specified time, PyCharge computes the retarded time of the point charges at each grid point, which are subsequently used to compute the analytical solutions to Maxwell's equations for each point charge. The Lorentz oscillators are driven by the electric field in the system and PyCharge…
An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on…
Working within the framework of the classical theory of electrodynamics, we derive an exact mathematical solution to the problem of self-field (or radiation reaction) of an accelerated point-charge traveling in free space. We obtain relativistic expressions for the self-field as well as the rates of radiated energy and linear momentum without the need to renormalize the particle's mass - or to discard undesirable infinities.
An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self 4-potential does not posses…
