Develop a theoretical description of particle–field interactions

Develop a set of governing equations that describe the mechanical–electromagnetic interaction between charged particles and the electromagnetic field, namely the coupled process of particle motion and electromagnetic field propagation, to replace non-relativistic instantaneous action-at-a-distance models in microscopic thermodynamic analyses.

Background

The paper argues that standard mechanical and electromagnetic formulations describe only actions under prescribed conditions (particles moving in a given field, or fields radiated by a given particle motion), not true interactions where particle dynamics and field evolution are coupled.

The author emphasizes that instantaneous action-at-a-distance potentials used in Hamiltonian mechanics are non-relativistic and inadequate, and highlights unresolved issues such as radiation reaction and the Lorentz–Dirac equation as reflections of the missing interaction framework.