Effective dynamics of a classical point charge

Abstract

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham-Lorentz force is recovered and its similarity to anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.

Extended final version, to appear in Annals of Physics

References in corpus (3)

• Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space
• Quantum-classical crossover in electrodynamics
• Sub-classical fields and polarization in electrodynamics

Cited by in corpus (9)

• Classical and quantum effective theories
• Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles
• Universality of anomalous conductivities in theories with higher-derivative holographic duals
• Boost invariant regulator for field theories
• The Abraham-Lorentz force and electrodynamics at the classical electron radius
• Radiation reaction from quantum electrodynamics and its implications for the Unruh effect
• Second order equation of motion for electromagnetic radiation back-reaction
• Time scale of stationary decoherence
• Radiation Reaction as a Non-conservative Force