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Radiation reaction in higher-order electrodynamics

Alan Baza, Aaron DeLeon, Angel Harb, Vu Hoang, Maria Radosz

Abstract

This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Landé--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. The self-force coincides with an expression proposed by Zayats and Gratus--Perlick--Tucker on the basis of an averaging procedure.

Radiation reaction in higher-order electrodynamics

Abstract

This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Landé--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. The self-force coincides with an expression proposed by Zayats and Gratus--Perlick--Tucker on the basis of an averaging procedure.

Paper Structure

This paper contains 16 sections, 21 theorems, 209 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Field equations
  3. Notation and conventions
  4. Retarded solution of the field equations
  5. Retarded light-cone coordinates
  6. Energy-momentum tensor and fields
  7. The principle of Energy-Momentum conservation
  8. Distributional formulation
  9. Properties of self-field energy-momentum tensor
  10. Particle interactions
  11. Proof of Main Result (Theorem \ref{['thm_main']})
  12. Variational principle for retarded fields
  13. Local formulation
  14. Variation of retarded fields with particles
  15. Motion under influence of external forces
  16. ...and 1 more sections

Key Result

Proposition \oldthetheorem

Let $F^{ab}$ be the field tensor for a single particle world-line eq_field_tensor. Then we have where $U^a$ is the Liénard-Wiechert potential given by

Figures (3)

  • Figure 1: Intersection between particle world-line and backwards light cone
  • Figure 2: World-tube
  • Figure 3: A world-line $q^{\alpha}(\tau)$ and a variation $Q^\alpha(\tau,\sigma)$ in $\Omega$. White area: $\chi=1$, light grey area: $0<\chi< 1$, dark grey area: $\chi=0$.

Theorems & Definitions (54)

  • Definition \oldthetheorem
  • Remark \oldthetheorem
  • Proposition \oldthetheorem
  • proof
  • Proposition \oldthetheorem
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • ...and 44 more