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 the radiation phenomena and charges' equations of motions where the radiation reaction is taken into account. The intended audience is physicist who works in relative fields or graduate student who wants a short exposition of classical electrodynamics in the language of coordinate-free differential geometry.

Comprehensive graduate-level text by a distinguished theoretical physicist reveals the classical underpinnings of modern quantum field theory. Topics include space-time, Lorentz transformations, conservation laws, equations of motion, Green’s functions, and more. 1964 edition.

This thesis presents several important aspects of the plasma dynamics in extremely high intensity electromagnetic fields when quantum electrodynamics effects have to be taken into account. This work is of utmost importance for the forthcoming generation of multipetawatt laser facilities where this physics will be tested. The first part consists of an introduction that extends from classical and quantum electrodynamics in strong fields to the kinetic description of plasmas in the interaction with such fields. This can be considered as an advanced tutorial which would be extremely useful to researchers and students new to the field. The second part describes original contributions on the analysis of the signatures of classical and quantum radiation reaction on the distribution function of the charged particles and of the photon spectrum, and leads to significant advances on this topic. These results are then extended to the analysis of the so-called QED cascades which are of central importance for a better understanding of some astrophysical phenomena and basic physics problems. Finally, the book discusses future directions for the high intensity laser–plasma interaction community. The results presented in this thesis are expected to become more and more relevant as the new multipetawatt facilities become operative.

Widely-discussed in the theory of classical point charges are the difficulties of divergent self-energy, self-accelerating solutions, and pre-acceleration. This book explains the theory in the context of quantum electrodynamics, the neutral particle limit, and coherence with neighboring theories.

A mathematical procedure is given for singling out the causal solutions from the general set of solutions of self-adjoint differential equations. It consists in splitting the self-adjoint equation into a pair of adjoint equations whose solutions are purely causal and purely anti-causal, respectively. A subsequent merging of the equations then generates in full detail, including singularities, the causal and anti-causal :olutions of the original self -adjoint equation. As an important example, it is shown that the d'Alembertian with point source has a legitimate causal solution involving both retarded and advanced potentials at the source point itself, while at all other points, the retarded potential alone satisfies causality. Within the context of the formalism some recent attempts at modifying classical radiation theory can now be reassessed and more clearly categorized. In particular, the Dirac and Wheeler-Feynman approaches are examined in this light.

Originally written in 1964, this famous text is a study of the classical theory of charged particles. Many applications treat electrons as point particles. At the same time, there is a widespread belief that the theory of point particles is beset with various difficulties such as an infinite electrostatic self-energy, a rather doubtful equation of motion which admits physically meaningless solutions, violation of causality and others. The classical theory of charged particles has been largely ignored and has been left in an incomplete state since the discovery of quantum mechanics. Despite the great efforts of men such as Lorentz, Abraham, Poincar‚, and Dirac, it is usually regarded as a ?lost cause?. But thanks to progress made just a few years ago, the author is able to resolve the various problems and to complete this unfinished theory successfully.