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Suppose an electron is producing an electric field by emission of virtual photons and interacting with other particles. What parameters determine the probability that it will emit at least one virtual photon in a time period of length $T$? What is the formula for this probability?

Qmechanic
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Alex L
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  • maybe this answer of mine will help https://physics.stackexchange.com/q/185110/ – anna v May 07 '19 at 03:42
  • @anna Thanks. My question was, what is the probability of repulsion in the case of two electrons? – Alex L May 07 '19 at 03:47
  • that is calculated by integrating the Feynman diagrams, to first order the diagram shown in the link. – anna v May 07 '19 at 03:48
  • @anna is there anywhere I can find the calculations? – Alex L May 07 '19 at 03:51
  • there is an infinity of virtual photons mathematically "exchanged",you do not have one virtual ever. – anna v May 07 '19 at 03:51
  • About calculation, I suppose in courses on quantum field theory it will be one of the first exercises. here is one online https://ocw.mit.edu/courses/physics/8-323-relativistic-quantum-field-theory-i-spring-2008/ – anna v May 07 '19 at 03:54

1 Answers1

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The famously dimensionless fine-structure constant

$$\alpha=\frac{1}{4\pi\epsilon_0}\frac{e^2}{\hbar c}\approx\frac{1}{137.036}$$

is the probability that an electron or positron emits or absorbs a photon, when one calculates Feynman diagrams.

G. Smith
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  • Can one calculate the probability that the electron emits or absorbs a virtual photon in a time period of length T? I mean, what is exactly 1/137, the probability that the electron emits/absorbs a virtual photon in a certain time period, or at any moment, or etc? – Alex L May 08 '19 at 05:00
  • The probability that an electron emits or absorbs a virtual photon in a time period $T$ is not well-defined. It depends on what the electron is doing. And nobody does calculations like that as far as I know. – G. Smith May 08 '19 at 05:23
  • In QED, one typically calculates the probability of various scattering processes over an infinite amount of time where particles come together from infinity, interact, and move apart to infinity. These calculations involve the probability amplitude that various particles propagate from one place to another and the probability amplitude that they interact with each other. Every electron-photon interaction introduces a factor of $\alpha$ into the overall probability of the process. – G. Smith May 08 '19 at 05:23