Related papers: On the two body problem in the classical electrody…
We present a new view for duality in classical electromagnetic theory, based on the physical properties of a dual theory, eliminating the problems of the usual treatment of the subject.
In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here we revise and explain some of the paradoxical issues that one faces when…
In the direct action form of classical EM we give the equation of motion for a classical massless bare charge without self-interaction in the presence of an external field. That equation permits superluminal speeds and time-reversals, and…
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…
We consider two-body problem in the self-field (1+1)-dimensional quantum electrodynamics on the circle. We present two formulations of the problem which correspond to two different types of variational principles and prove that both…
As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the…
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point…
The classical electrodynamic system of field and a single point-like source is considered in even-dimensional space-time. The problem of self-interaction is discussed. It is manifestly shown that all singular terms appearing in these…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…
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…
Solutions of classical and quantum equations of motion in spinor electrodynamics are constructed within the context of perturbation theory. The solutions possess a graphical representation in terms of diagrams.