Electrodynamics of massless charged particles

Understand

We derive the classical dynamics of massless charged particles in a rigorous way from first principles.

• Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b) Lorentz- and reparameterization-invariance, c) local conservation of energy and momentum.
• Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor.
• Its conservation requires the particles to obey standard Lorentz equations and they experience, hence, no radiation reaction.