Covariant Electromagnetism in Past-Light-Cone Formalism

TL;DR

This paper introduces a covariant formalism for relativistic electromagnetism that computes electromagnetic fields from moving charges using past light cone intersections, ensuring Lorentz covariance and causal consistency.

Contribution

It presents a new covariant formulation of electromagnetism based on past light cone intersections, generalizing Lie9nard-Wiechert potentials for improved computational implementation.

Findings

Provides a covariant generalization of Lie9nard-Wiechert potentials.

Ensures causal consistency in electromagnetic field calculations.

Facilitates direct computer implementation of relativistic electromagnetism.

Abstract

We present a manifestly covariant formulation of relativistic electromagnetism, focusing on the computation of electromagnetic fields from moving charges in a manifestly Lorentz-covariant manner. The electromagnetic field at a given spacetime point is determined by the motion of point charges at the intersection of their worldlines with the past light cone of the spacetime point, ensuring causal consistency. This formalism provides a manifestly covariant generalization of the Li\'enard-Wiechert potentials and allows direct implementation on computers. We compare our formulation with standard textbook approaches and analyze its behavior in various physical limits.