Radiation reaction, renormalization and conservation laws in six-dimensional classical electrodynamics (original) (raw)
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Radiation reaction and renormalization via conservation laws of the Poincaré group
Journal of Physical Studies
We consider the self-action problem in classical electrodynamics of a point-like charge arbitrarily moving in flat space-time of four or six dimensions. A consistent regularization procedure is proposed which exploits the symmetry properties of the theory. The energy-momentum and angular momentum balance equations allow us to derive the radiation reaction forces in both 4D and 6D. It is shown that a pointlike source in 6D possesses an internal angular momentum with magnitude which is proportional to the square of acceleration. 6D action functional contains, apart from usual "bare" mass, an additional renormalization constant which corresponds to the curvature of the world line (i.e. to the magnitude of internal angular momentum of "bare" particle). It is demonstrated that the Poincaré-invariant six-dimensional electrodynamics is renormalizable theory.
Radiation Reaction and Renormalization via Conservation Laws of the Poincar� Group
2004
We consider the self-action problem in classical electrodynamics of a point-like charge arbitrarily moving in flat space-time of four or six dimensions. A consistent regularization procedure is proposed which exploits the symmetry properties of the theory. The energy-momentum and angular momentum balance equations allow us to derive the radiation reaction forces in both 4D and 6D. It is shown that a pointlike source in 6D possesses an internal angular momentum with magnitude which is proportional to the square of acceleration. 6D action functional contains, apart from usual "bare" mass, an additional renormalization constant which corresponds to the curvature of the world line (i.e. to the magnitude of internal angular momentum of "bare" particle). It is demonstrated that the Poincaré-invariant six-dimensional electrodynamics is renormalizable theory.
Physical Review D, 2002
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d = 4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.
Radiation reaction in higher-order electrodynamics
2021
This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Lande–Thomas, and Podolsky. We rigorously derive a world line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. Our work thus gives a rigorous vindication of an expression for the self-force first proposed by Lande and Thomas, studied by Zayats for straight line motion, and, more generally, obtained by Gratus, Perlick, and Tucker on the basis of an averaging axiom.
Radiation Reaction, Renormalization and Poincaré Symmetry
Symmetry, Integrability and Geometry: Methods and Applications, 2005
We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is proposed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincaré-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields, which do not change the velocity of the particle, admit only its presence within the interaction area. The effective equation of motion is the equation for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the effect of combination of outgoing electromagnetic waves generated by the charges.
Radiation reaction in 2+1 electrodynamics
Journal of Mathematical Physics, 2007
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 charge constitute the total conserved quantities of our particle plus field system. Their differential consequences yield the effective equation of motion of radiating charge in an external electromagnetic field. In this integrodifferential equation the radiation reaction is determined by Lorentz force of pointlike charge acting upon itself plus nonlocal term which provides finiteness of the self-action.
The European Physical Journal Plus, 2011
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 selffield 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 possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed respectively in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.
1 0 A ug 2 02 0 Electrodynamics in flat spacetime of six dimensions
2020
We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we establish the algebraic structure of electromagnetic field in 6D. We elaborate the classification scheme based on three field’s invariants. Using the basic algebraic properties of the electromagnetic field tensor we analyze the motion of a charge in constant electromagnetic field. Its world line is a combination of hyperbolic and circular orbits which lie in three mutually orthogonal sheets of two dimensions. Within the braneworld scenario, we project the theory on the de Sitter space of four dimensions. Actually, as it turns out, spins of elementary particles themselves are manifestations of extra dimensions.
Physical Review D, 2006
We extend our previous work (see arXiv:quant-ph/0501026), which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion. Specifically, we calculate the predictions for the change in position of a charged scalar particle, moving in three-dimensional space, due to the effect of radiation reaction in the one-photon-emission process in quantum electrodynamics. The scalar particle is assumed to be accelerated for a finite period of time by a three-dimensional electromagnetic potential dependent only on one of the spacetime coordinates. We perform this calculation in theh → 0 limit and show that the change in position agrees with that obtained in classical electrodynamics with the Lorentz-Dirac force treated as a perturbation. We also show for a time-dependent but space-independent electromagnetic potential that the forward-scattering amplitude at order e 2 does not contribute to the position change in theh → 0 limit after the mass renormalization is taken into account.
Radiation Reaction in Classical Field Theory
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 electrodynamics in four dimensions (one time dimension and three spatial ones), we consider exotic worlds of dimensions other than four which arise in various research areas, e. g. in string theory, physics of graphene, dynamics of superfluid 4He film etc. Thorough analysis is given to radiation phenomena and charges' equations of motions where the radiation reaction is taken into ac...