Which classical radiation-reaction equation is the classical limit of QED? · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title · changed
Revision 1: Which classical radiation-reaction equation is the classical limit of QED
Revision 2: Which classical radiation-reaction equation is the classical limit of QED?
Plain
The classical Abraham-Lorentz-Dirac equation predicts electrons that run away or accelerate before a force arrives, so physicists use a cleaned-up version, the Landau-Lifshitz equation. The question is which equation quantum theory actually reduces to when quantum effects are switched off.
Precise · changed · core
Revision 1: The Lorentz-Abraham-Dirac (LAD) equation, third order in time with characteristic time $\tau_0 = 2 e^2/(3 m c^3) \sim 6.3e-24\,\mathrm{s}$, has runaway and preaccelerating solutions; restricting LAD to its non-runaway (critical) manifold gives a second-order equation whose first-order approximation in $\tau_0$ is the Landau-Lifshitz (LL) equation; the two differ from order $\tau_0^2$ on. Determine the classical limit ($\hbar \to 0$ at fixed classical field parameters) of QED for a point charge in a background field to all orders in $\tau_0$, and identify whether it coincides with LL, with LAD on the critical manifold, or with another second-order equation (for example Ford-O'Connell), at orders beyond the leading one in $\alpha$.
Revision 2: The Lorentz-Abraham-Dirac (LAD) equation, third order in time with characteristic time $\tau_0 = 2 e^2/(3 m c^3) \sim 6.3 \times 10^{-24}\,\mathrm{s}$, has runaway and preaccelerating solutions; restricting LAD to its non-runaway (critical) manifold gives a second-order equation whose first-order approximation in $\tau_0$ is the Landau-Lifshitz (LL) equation; the two differ from order $\tau_0^2$ on. Determine the classical limit ($\hbar \to 0$ at fixed classical field parameters) of QED for a point charge in a background field to all orders in $\tau_0$, and identify whether it coincides with LL, with LAD on the critical manifold, or with another second-order equation (for example Ford-O'Connell), at orders beyond the leading one in $\alpha$.
Settled by
A derivation from QED in a general (at least plane-wave) background of the classical equation of motion to second and higher order in $\tau_{0}$, compared term by term with LL and with the critical-manifold reduction of LAD.
Kind
well-posed
Answer type
identification
References
(empty)
Literature status
partially-resolved
Status note
The LL equation has been recovered from QED at leading order in $\alpha$ in plane-wave backgrounds; I do not have a verified source for an all-order result as of 2026.
Posed since
(empty)

Decisions