2021/12/31 by Robin Ekman
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Coupling (piping) #Dirac (video compression format) #Dirac equation #Engineering #High-pressure geophysics and materials #Laser-Matter Interactions and Applications #Laser-Plasma Interactions and Diagnostics #Lorentz transformation #Mathematical physics #Mathematics #Order (exchange) #Physics #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Reduction (mathematics) #Resummation #hep-ph #hep-th #physics.plasm-ph
paper · pdf · doi:10.1103/physrevd.105.056016
v2: extended discussion of runaway solutions v3: typos corrected
arxiv created 2022/03/22 · openalex publication_date 2022/03/24 · arxiv updated 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Landau-Lifshitz equation is obtained from the Lorentz-Abraham-Dirac equation through `reduction of order'. It is the first in a divergent series of approximations that, after resummation, eliminate runaway solutions. Using Borel plane and transseries analysis we explain why this is, and show that a non-perturbative formulation of reduction of order can retain runaway solutions. We also apply transseries analysis to solutions of the Lorentz-Abraham-Dirac equation, essentially treating them as expansions in both time and a coupling. Our results illustrate some aspects of such expansions under changes of variables and limits.