Work and energy for particles in electromagnetic field

Abstract

Defining the energy and work for particles interacting with electromagnetic field (EMF) is an open problem, because—due to the gauge-freedom—there exist various non-equivalent possibilities. It is argued that a consistent definition can be provided via the Lorenz gauge. To this end, I work out a system of two electromagnetically coupled classical particles. One of them is much heavier and models the source of work. The definition of energy in the Lorenz gauge is causal and consistent, because it leads to an approximate conservation law due to which the work done by the heavy particle (source of work) can be defined either via the kinetic energy of the heavy particle, or via the full time-dependent energy (kinetic + potential in the Lorenz gauge) of the light particle.