Covariant Electromagnetism in Past-Light-Cone Formalism

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.