Regularization of the collision in the electromagnetic two-body problem.

Area of Science:

• Theoretical Physics
• Computational Physics
• Electrodynamics

Background:

• Relativistic action-at-a-distance electrodynamics involves complex two-body interactions.
• Simulating collisions in such systems presents mathematical challenges due to singularities.
• Historical context includes foundational work by Dirac, Wheeler, and Feynman.

Purpose of the Study:

• To derive a regular differential equation for the collision of two equal-mass bodies.
• To develop a stable numerical method for calculating collision orbits.
• To analyze the physics of this conservative dynamical system.

Main Methods:

• Derivation of a regular differential equation using Poincaré invariance and energy constants.
• Definition of finite variables and derivatives at the point of collision.
• Numerical calculation of collision orbits via a self-consistent minimization method.

Main Results:

• A regularized differential equation applicable to two-body collisions in relativistic electrodynamics.
• Successful numerical computation of collision orbits using a stable, non-runaway solution selection method.
• Demonstration of finite variables and derivatives at the collision point.

Conclusions:

• The derived regular equation provides a robust method for studying relativistic two-body collisions.
• The numerical approach ensures stability and accuracy in simulating complex dynamical systems.
• This work advances the understanding of covariant time-symmetric two-body dynamics.