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How does the spin state of the electron affect the polarisation of the light emitted?

I am looking for a description in a detailed mathematical aspect, any suggestions on books ?

I'm Batman
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  • I just ran across a new concept on electron spin by Charles Sebens. How Electrons Spin. https://arxiv.org/abs/1806.01121 He says that it is not the electron that spins, but rather the Dirac field surrounding the electron. Interesting take. Originally found in Scientific American https://www.scientificamerican.com/article/quantum-particles-arent-spinning-so-where-does-their-spin-come-from/ – foolishmuse Nov 29 '22 at 23:08
  • If you’re interested in a classical analysis of the EM radiation emitted by an accelerating magnetic dipole, this paper may be of interest. You could combine this field with the standard field of an accelerating charge, since a spinning electron has both a charge and a magnetic moment. – Ghoster Nov 29 '22 at 23:31
  • If you’re interested in some quantum process involving one or two photons, you should specify more precisely what you have in mind. What is happening to the electron that is causing it to emit photons? – Ghoster Nov 29 '22 at 23:34
  • @foolishmuse Sebens is an assistant professor of philosophy at Caltech. His preprint was relegated to General Physics on arXiv, which is often where questionable papers get put. The paper is not being published in a physics journal after peer review by physicists, but in a history and philosophy journal. It is possible/likely that his paper will be mostly ignored. Many physicists will assume he couldn’t get it published in a reputable physics journal. – Ghoster Nov 30 '22 at 00:42
  • @Ghoster I think Sebens's paper is correct, or at least not entirely wrong. See Ohanian (Am. J. Phys., 1986) and this answer. I doubt anything in the paper is really new, and that could be why it didn't make it into a physics journal, but I'm only guessing. – benrg Nov 30 '22 at 02:05
  • @foolishmuse See my previous comment. – benrg Nov 30 '22 at 02:05
  • The question is vague. If the the final state photon needs to be in a spin eigenstate (J=1), it will be circularly polarized, but what is the transition? – JEB Nov 30 '22 at 02:33
  • @Ghoster. I first saw mention of the paper in a long article in scientific American magazine. Does this not meet your standards? Personally, I don't hold a lot of stock in whether an interesting theory has been published or not. If you're not standing on the edge, you're taking up too much room. – foolishmuse Nov 30 '22 at 02:38
  • I didn’t opine on whether Sebens is right or wrong. I opined that it is likely his paper will have minimal impact because it isn’t in a physics journal. I used to think Sci Am was a good popular science mag decades ago, but I don’t think much of it any more; it’s been dumbed down to get greater readership. It has never been a physics journal. – Ghoster Nov 30 '22 at 04:06
  • There is angular momentum conservation, which results in Selection rules (which is your keyword for looking up book material). These usually involve also orbital momentum, since an electron not bounded by an atom or a lattice does not emit photons. – Roger V. Dec 01 '22 at 08:45
  • @Ghoster Seben's point of view is not new, and that kind of interpretation of the spin was advanced in the past by physicists such as Beiinfante (1939) and more recently by Ohanian, to cite two of them. Seben published his views in many papers that appeared in different journals. I think that every judgment on these papers and their possible relevance should be based on their physical content and not on the journal-title. Anyway, the relevance of Seben's point of view for this question is marginal. it is only a useful reminder that the spin status is a property of the state. – GiorgioP-DoomsdayClockIsAt-90 Dec 05 '22 at 08:43
  • @GiorgioP the relevance of Seben's point of view for this question is marginal Agreed! I wasn’t the one who brought up this irrelevant paper. The paper I mentioned — on the radiation from accelerating magnetic dipoles — was highly relevant to the OP’s question. – Ghoster Dec 05 '22 at 20:07

2 Answers2

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An interesting question that I want to answer for the emission of photons in the case of the Lorentz force or Hall effect.

Electrons are aligned in the magnetic field with their magnetic dipole to the external magnetic field. As is known, an electron moving through the external field will emit photons and will be deflected sideways. The resulting EM radiation is polarised. Best studied in radiation from synchrotrons and other particle accelerators.

Conversely, it should be noted that from the polarised radiation of radio antennas, conclusions can be drawn about the behaviour of the surface electrons on an antenna rod. These electrons are aligned with their magnetic dipoles during their cyclic accelerations, otherwise there would be no emitted polarised radio wave.

You ask about spin and have to replace the term magnetic dipole from my answer with spin. If you think that is more intuitive or otherwise necessary.

Unfortunately, I can't help with mathematics. So take it more as a long comment than an answer.

HolgerFiedler
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I found a better description of the same in book by Bransden and Jochain. The spin of the electron changing is transferred to the photon. and a beutiful mathematical description is shown in the book.

Specifically, in the section.. 4.5 where the selection rules are discussed and the rules for angular momemntum of the photon is elaborated.

I'm Batman
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  • Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. – Community Jan 21 '23 at 17:19