Classical and Quantum Radiation Reaction for Linear Acceleration

Abstract

We investigate the effect of radiation reaction on the motion of a wave packet of a charged scalar particle linearly accelerated in quantum electrodynamics. We give the details of the calculations for the case where the particle is accelerated by a static potential that were outlined in Phys. Rev. D 70 (2004) 081701(R) and present similar results in the case of a time-dependent but space-independent potential. In particular, we calculate the expectation value of the position of the charged particle after the acceleration, to first order in the fine structure constant in the → 0 limit, and find that the change in the expectation value of the position (the position shift) due to radiation reaction agrees exactly with the result obtained using the Lorentz-Dirac force in classical electrodynamics for both potentials. We also point out that the one-loop correction to the potential may contribute to the position change in this limit.

Quantum corrections to the Larmor radiation formula in scalar electrodynamics

“…[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.)…”

“…where the function analogous to the varying energy σ p (t) in the time-dependent case is now a varying z-component of the momentum, 2) and where p = p 0 2 − |p ⊥ | 2 − m 2 . As in the case with a time-dependent vector potential, it can be shown that higher-order corrections to Eq.…”

“…Since classical electrodynamics is an approximation to quantum electrodynamics (QED), one expects that the Larmor formula should be reproduced in the latter theory in the limit → 0 (at order e 2 ). 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.…”

“…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.…”

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

“…The model is the three-dimensional extension of that used in Refs. [11,12] with the potential dependent only on one of the space-time coordinates, x a say. The particle is accelerated by an external force arising from an electromagnetic potential V µ .…”