Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics

Abstract

We extend our previous work (see arXiv:quant-ph/0501026), which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-LorentzDirac theory for a charged particle in linear motion. Specifically, we calculate the predictions for the change in position of a charged scalar particle, moving in three-dimensional space, due to the effect of radiation reaction in the one-photon-emission process in quantum electrodynamics. The scalar particle is assumed to be accelerated for a finite period of time by a three-dimensional electromagnetic potential dependent only on one of the spacetime coordinates. We perform this calculation in theh → 0 limit and show that the change in position agrees with that obtained in classical electrodynamics with the Lorentz-Dirac force treated as a perturbation. We also show for a time-dependent but space-independent electromagnetic potential that the forward-scattering amplitude at order e 2 does not contribute to the position change in theh → 0 limit after the mass renormalization is taken into account.

Quantum corrections to the Larmor radiation formula in scalar electrodynamics

“…Indeed it has been shown that this formula is recovered in QED for a scalar charged particle moving on a straight line in the limit → 0 [2]. Furthermore it has been shown [3,4] that the Lorentz-Dirac radiation-reaction force [5,6,7] is obtained in the limit → 0 in QED for a scalar charged particle in three-dimensional motion under the influence of a vector potential depending only on one spacetime coordinate. (For other approaches for studying the Lorentz-Dirac force in the context of QED, see Refs.…”

“…Therefore, if A (n−1) 3 tends to zero as a → 0, so does A (n) 3 . This means that all we need to show is A …”

“…[2,3] closely. (The derivation for the case with a potential which depends on one space coordinate will not be presented, but it is very similar to the case treated here.)…”

“…The purpose of this paper is to carry out this task in the simple setting used in Refs. [2,3,4] where the scalar particle is accelerated by a vector potential that depend only on one spacetime coordinate under the additional condition that the initial state of the charged particle is a momentum eigenstate.…”

Role of momentum and velocity for radiating electrons

“…Given the success of QED, some authors have explored whether its classical limit can shed light on the question of the correct theory of radiation reaction [42][43][44][45]. In [46], the QED predictions for an electron interacting with a plane electromagnetic wave have been compared with those of a range of classical theories, including LL and Sokolov.…”