2

In the virtual particles FAQ here https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html, under "How can they be responsible for attractive forces?" I didn't follow this step:

"If the wave packet is small enough in position space, a Coulomb potential and a sinusoidal one are both effectively a constant-force potential, so I can do this.  Neglecting all magnetic effects and taking the nonrelativistic limit, the amplitude for transfer of a given momentum by a single virtual photon […] has to have an imaginary part odd in p_x because the potential is real,…"

How is this oddness derived? Or, what do I need to know/study to derive this?

Added:

More precisely, I would like to understand first of all, what is the right equation to write down from QM theory, and what are the modifications (neglecting magnetic effects, taking limit, etc.) we should make for this simplified model? And secondly, if it's not already clear, how do I get from there, to an approximation by an odd function (whose sign depends on parity) such as is necessary to follow the rest of the thought experiment in the FAQ?

(My real goal here isn't to pick apart this FAQ, but to understand how attractive force comes from QM first principles, I'm just not knowledgeable enough to fill in the gaps of the FAQ. If there is another more detailed treatment of this topic to recommend that would also be helpful.)

Ben
  • 121
  • 3
    Does this answer your question? Force carrier particle exchanges and attraction – ZeroTheHero Feb 15 '21 at 01:31
  • Classical field theory has virtual particles in essentially the same sense that quantum field theory does, even though classical field theory doesn't have particles. Seeing how this works can help resolve clarify the whole virtual particle topic, including how they can produce attractive forces. For a place to start, see the last section in https://www.mat.univie.ac.at/~neum/physfaq/topics/feynman.html (written by @ArnoldNeumaier), which cites https://homepages.physik.uni-muenchen.de/~helling/classical_fields.pdf. – Chiral Anomaly Feb 15 '21 at 03:00
  • Based on the points I was confused on reading McIrvin's FAQ article, I think OP's question probably should be rephrased to focus in and ask precisely what Matt McIrvin meant by "potential" when he wrote that statement, why that "potential" is real, and how does that real potential leads to an imaginary part of the "amplitude for transfer of a given momentum by a single virtual photon" that is odd in $p_x$. The whole thing is evocative of a Fourier transform, but it doesn't seem like McIrvin is saying the Fourier transform of $p_x$ is a real potential, which leads to my personal confusion. – Jonathan Jeffrey Feb 15 '21 at 03:04
  • Put it this way: the title doesn't represent the question well, because the question is about a few specific details in "a note for experts only" that McIrvin wrote. I would think OP wants to understand what leads to those details in that specific step, not the general picture, because McIrvin's article already explains the general picture really well. – Jonathan Jeffrey Feb 15 '21 at 03:07
  • @ZeroTheHero I don't think it quite answers the question I meant to ask. I'd like to know more about the relevant "QM perturbative calculation, whose covariant expression is symbolically summarized by a Feynman diagram" of that question. My understanding is this is what McIrvin is calculating (approximately, in a toy model) in the FAQ, but I'm not sure what that calculation is, or what approximation of it is being made. – Ben Feb 15 '21 at 05:01
  • @ChiralAnomaly Thank you for the links, I will take a look at the Helling article and see if I can find what I'm looking for there. – Ben Feb 15 '21 at 05:10
  • 1
    @JonathanJeffrey Thank you for the feedback, the title was not very good - I will see if I can edit or ask a new question. I found the FAQ a convincing reduction of the problem to the claimed shape of the photon wave function, but I wanted to understand it all from first principles as much as possible. So I meant to ask about how to get from e.g. a Schrodinger equation to the (odd) function described in the FAQ. – Ben Feb 15 '21 at 05:19
  • @Ben, Case in point, looks like people thought this was a duplicate to the linked question, even though it isn't. So, yeah, either edit or ask a new question. – Jonathan Jeffrey Feb 15 '21 at 05:34
  • @JonathanJeffrey Thank you, I have edited the question now. (My apologies to all the maintainers for not making a better first effort) – Ben Feb 15 '21 at 05:45
  • @ZeroTheHero is it possible to reopen? – Ben Feb 16 '21 at 12:15

0 Answers0