# Radiation reaction in the classical limit of QED?

## Main Question or Discussion Point

The classical problem of radiation reaction classical electrodynamics seems to be a huge mess with no good answer. There is no even consensus of the very form of the Newton law "predicted" theory.

So, the question of this thread is: Does the classical limit of QED say something about this topic?, is there a limit of QED where we recover a Newton-like equation that includes radiation reaction effect?

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

DrClaude
Mentor
I am in no way qualified to answer your question, but I found the following paper which appears to address the topic:

Greger Torgrimsson
Quantum and Classical Radiation Reaction from Lightfront QED
Abstract: We examine dynamical radiation reaction in lightfront QED. We take the classical limit and compare with predictions from various classical equations of motion.

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A. Neumaier
2019 Award
I found the following paper which appears to address the topic
It indeed completely answers the question.

Hi, thanks for the article, it seems informative in itself. However, I don't see the relation to the question asked in the OP, there is no mention of QED in it.
There was supposed to be a second link posted with it on the subject.

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.3423

Sorry I was in a hurry and didn't proof read. I don't know much about this or any other field of physics study. So I figured I'd look something up for ya. Usually all it takes to get the ball rolling here is a reply. Even if its an incorrect one. Sometimes that works faster. lol

The classical problem of radiation reaction classical electrodynamics seems to be a huge mess with no good answer. There is no even consensus of the very form of the Newton law "predicted" theory.

So, the question of this thread is: Does the classical limit of QED say something about this topic?, is there a limit of QED where we recover a Newton-like equation that includes radiation reaction effect?
An electron's motion would be affected by radiation reaction much less than its own inertia unless the frequency is comparable to c/r_0, were r_0 is the classical electron radius. However one can never observe this in the classical regime, as a single photon at this frequency has an energy of ~137mc^2 and the recoil from the emission of this photon is itself relativistic.

In order to get the electron to oscillate at a frequency this high, you need to hit it with electromgnetic fields this fast. But with a photon energy of 137mc^2 (70 MeV) we are deep into the quantum regime (Thomson scattering, the classical EM process, turns into Compton scattering when the photon energy approaches or exceeds mc^2, or about 0.511 MeV. At this point the classical rate of radiation emission must be replaced by the Klein-Nishina formula).

vanhees71
Gold Member
2019 Award
Of course, there's "soft bremsstrahlung" either. For that you need to tame IR and collinear singularities in the quantum theory, but that's more an issue of using the wrong asymptotic states. The right asymptotic states in QED are not plane waves but something like coherent states. The reason is that the photon is massless and thus the electromagnetic interaction longranged (in the vacuum).

Using perturbation theory this leads to the usual soft-photon resummations. For a very good introduction, see Weinberg, QT of Fields, vol. I.

tIn the case of soft bremsstrahlung, one only can observe the average energy loss in a large number of collisions (say, by measuring the rate at which a plasma cools by emitting bremstrahlung), which is not the same as observing the effects of radiation damping forces during the scattering process itself. The "unsolved" aspect of the problem in classical electrodynamics involving runaway solutions or acausal preacceleration does not show up in the low-frequency regime, and the effects of classical radiation damping are small, deflecting the electron trajectory by a miniscule amount compared to the Coulomb scattering event which gave rise to the bremsstrahlung in the first place. Thus, apart from its statistical effects on energy loss, "true" classical radiation damping is not observable in bremsstrahlung .

Another way of looking at it is that the Schott energy term in the radiation damping equation is a correction to the elecron mass-energy which presumably should impact the Coulomb scattering cross section since the latter depends on electron mass, but a simple back-of-the-envelope calulation shows that this effect is far too small to measure it in the lab, sadly. Thus, no experiment involving bremsstrahlung in the classical regime can distinguish between competing models of RR forces or confirm the existence of the Schott energy of the electron.

Even disregarding lack of experimental access and only considering QED vs. classical theory, it is far from clear (to me) at what QED order one could distinguish between competing classical expressions for the RR force (which both result in the same average energy loss and this energy loss is recreated in the soft photon limit of QED perturbation theory).

The classical expressions which differ in their handling of the Schott energy term but which have the same overall energy loss to lowest order are the ones we want to distinguish.

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