Radiation of an accelerated charge

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When a charge is accelerated, it radiates photons, but the nature of this radiation in quantum mechanics raises questions about its continuity and quantization. The discussion centers on whether an electron moving between charged plates emits photons continuously or in discrete quanta, suggesting a misunderstanding of the electromagnetic field's behavior. Additionally, the direction of emitted radiation from a briefly accelerated charge is debated, with implications for energy conservation and the effects of the Heisenberg uncertainty principle. The conversation highlights the distinction between classical and quantum treatments of particle acceleration and radiation. The need for further exploration of quantum field theory (QFT) and relevant textbooks is acknowledged.
fluidistic
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I'm asking this question in the quantum physics part because I'd like a quantum related answer.
When a charge is accelerated, it will radiate photons. In my belief, it must radiate continuously as long as it's accelerated.
Maybe I'm getting a wrong picture. Imagine an electron moving through empty space between 2 opposite charged plates (capacitor). It will be accelerated toward one plate. But since I had not took any serious quantum course, I don't know if the E field between the plate is really continuous or made of EM waves or whatever I can imagine. Thus I'm not 100% sure if the electron will be accelerated at any moment, or by quanta. If it is accelerated at any moment, it should emit continuously I believe... Producing infinitely many photons, which doesn't occur obviously. Therefore I'm missing someting.
Another question: When a charge is accelerated very shortly, its speed will increase, it will emit at least 1 photon... but in what direction? Is that random? Or opposite to the direction motion of the accelerated particle, so that the speed of the charge gets lower than the speed it had right after the acceleration? And if so, is the speed of the particle the same as it was before the acceleration? If so, it would mean that the energy required to accelerate the electron has been 100% converted into a single photon and that the electron's motion remains unchanged... But with Heisenberg's uncertainty principle, I guess I'm far from guessing things right.

I'd appreciate any comment or any link/name of textbooks on the subjet.
Thanks a lot.
 
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Greg Bernhardt said:
@fluidistic did you find any more insight on this topic?
Yes, I completed all the undergraduate courses, including QM and EM. I don't have the books (Zangwill & Jackson) at hand to answer my questions right now.
My intuition regarding my last question tells me that the radiation will have a certain rotational symmetry and will not point randomly nor in a sharp direction.

Otherwise I seem to confuse a classical treatment of an electron with a QM or QFT treatment.

About the quantization of the E field, in QM I dealt with classical E field, but I think it can be quanticized in QFT.
 
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