An introduction to the Lorentz-Dirac equation

Abstract

These notes provide two derivations of the Lorentz-Dirac equation. The first is patterned after Landau and Lifshitz and is based on the observation that the half-retarded minus half-advanced potential is entirely responsible for the radiation-reaction force. The second is patterned after Dirac, and is based upon considerations of energy-momentum conservation; it relies exclusively on the retarded potential. The notes conclude with a discussion of the difficulties associated with the interpretation of the Lorentz-Dirac equation as an equation of motion for a point charge. The presentation is essentially self-contained, but the reader is assumed to possess some elements of differential geometry (necessary for the second derivation only).

14 pages, ReVTeX, 3 figures

Cited by in corpus (41)

• Gravitational wave snapshots of generic extreme mass ratio inspirals
• Dynamics of Emitting Electrons in Strong Electromagnetic Fields
• The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge
• Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension
• A Tail of a Quark in N=4 SYM
• Radiation reaction in quantum field theory
• Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics
• Radiation reaction for a massless charged particle
• Mass change and motion of a scalar charge in cosmological spacetimes
• Relativistic Kinematics and Stationary Motions
• Classical and quantum radiation reaction for linear acceleration
• The origin of the Schott term in the electromagnetic self force of a classical point charge
• Quasi-local contribution to the gravitational self-force
• The Lorentz-Dirac force from QED for linear acceleration
• An action for reaction in general dimension
• Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation
• Radiation reaction, renormalization and conservation laws in six-dimensional classical electrodynamics
• Electromagnetic Scoot
• Maxwell-Lorentz without self interactions: Conservation of energy and momentum
• Radiation-reaction in classical offshell electrodynamics: I. The above mass-shell case
• A second order differential equation for a point charged particle
• Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
• Classical and quantum radiation reaction in conformally flat spacetime
• Geometry of generalized higher order fields and applications to classical linear electrodynamics
• Radiation reaction reexamined: bound momentum and Schott term
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Radiation reaction in 2+1 electrodynamics
• Self force in 2+1 electrodynamics
• Radiation reaction and renormalization for a photon-like charged particle
• Interference of outgoing electromagnetic waves generated by two point-like sources
• Classical 5D fields generated by a uniformly accelerated point source
• Radiating particle in the vicinity of the weakly charged Schwarzschild black hole
• Self-force of a scalar charge in the space-time of extreme charged anti-dilatonic wormhole
• The alternative to classical mass renormalization for tube-based self-force calculations
• Relativistic Lagrangians for the Lorentz-Dirac equation
• Averaged dynamics of ultra-relativisitc charged particles beams
• Classical and Quantum Radiation Reaction
• Comment on "Dynamics of a Charged Particle"
• Problems in point charge electrodynamics
• Radiation effects on particle's trajectory in the linear level
• $\mathcal{C}$, $\mathcal{P}$, $\mathcal{T}$ operations and classical point charged particle dynamics