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

## Abstract

We extend our previous work [A. Higuchi and G. D. R. Martin, Found. Phys. 35, 1149 (2005)], which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-Lorentz-Dirac 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 the ({Dirac_h}/2{pi}){yields}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{sup 2} does not contribute to the position change in the ({Dirac_h}/2{pi}){yields}0 limit after the mass renormalization is taken into account.

- Authors:

- Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20795763

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.73.025019; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHARGED PARTICLES; COORDINATES; DISTURBANCES; MASS RENORMALIZATION; PHOTON EMISSION; POTENTIALS; QUANTUM ELECTRODYNAMICS; SCALARS; SCATTERING AMPLITUDES; SPACE; SPACE-TIME; THREE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE

### Citation Formats

```
Higuchi, Atsushi, and Martin, Giles D. R..
```*Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.0.

```
Higuchi, Atsushi, & Martin, Giles D. R..
```*Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics*. United States. doi:10.1103/PHYSREVD.73.0.

```
Higuchi, Atsushi, and Martin, Giles D. R.. Sun .
"Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics". United States.
doi:10.1103/PHYSREVD.73.0.
```

```
@article{osti_20795763,
```

title = {Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics},

author = {Higuchi, Atsushi and Martin, Giles D. R.},

abstractNote = {We extend our previous work [A. Higuchi and G. D. R. Martin, Found. Phys. 35, 1149 (2005)], which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-Lorentz-Dirac 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 the ({Dirac_h}/2{pi}){yields}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{sup 2} does not contribute to the position change in the ({Dirac_h}/2{pi}){yields}0 limit after the mass renormalization is taken into account.},

doi = {10.1103/PHYSREVD.73.0},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}