I'm currently taking the second part of a two semester course in quantum mechanics and while discussing the interaction of matter and radiation some Feynman diagrams came up. enter image description here The context is "lightscattering", meaning that we look at processes where a photon described by $\vec k, \lambda$ gets scattered into a photon $\vec k', \lambda'$, where $\vec k$ is the wave vector and $\lambda$ the polarization. The states $a$ and $b$ are one-particle states.

In the end we are interested in figuring out transition-amplitudes of the form $$\langle b; \vec k',\lambda'\vert e^{-iH(t-t_0)/\hbar}\vert a;\vec k,\lambda\rangle,$$ where the Hamiltonian is given by $$H=\frac{1}{2 m} \sum_{i}\left[\vec{p}_{i}-\frac{q_{i}}{c} \vec{A}\left(\vec{r}_{i}, t\right)\right]^{2}+\frac{1}{2} \sum_{i \neq j} \frac{q_{i} q_{j}}{\left|\vec{r}_{i}-\vec{r}_{j}\right|}+\int d^{3} r \frac{E_{\perp}^{2}+B^{2}}{8 \pi}$$

Now to the actual question: Can someone explain to me what is going on in (C)? I think I have an idea what is happening in (A) and (B), but when it comes to (C) I'm completely lost...


B and C simply differ in whether the charged particle absorbs the photon with momentum $k$ before or after it emits the photon with momentum $k’$.

  • $\begingroup$ It's been a while. Pretty hazy.. But I seem to recall there's some difference in polarization, directions of spins, or something like that. Anybody? I could be totally out of it here, but I seem to recall this is relevant to one of the "big name" tests of Bell's theorem. $\endgroup$
    – puppetsock
    Jun 19 '19 at 19:39
  • $\begingroup$ In both B and C you have to deal with the polarizations of the charged particle (unless it has spin $0$) and the polarizations of the photons. $\endgroup$
    – G. Smith
    Jun 19 '19 at 19:51
  • $\begingroup$ Just to be sure, there is a point where the two photon-lines „intersect“... What is this supposed to be? As far as I understand photons can‘t interact with each other (since they have no charge..), so how am I supposed to read that vertex.. $\endgroup$
    – Sito
    Jun 19 '19 at 19:57
  • 1
    $\begingroup$ That isn’t a vertex. There is nothing happening there. Imagine the two photons as not being in the same plane. It’s like in circuit diagrams where sometimes wires “cross” each other without being connected. $\endgroup$
    – G. Smith
    Jun 19 '19 at 20:00
  • $\begingroup$ What I am confused about is diagram A. If the charged particle is an electron, there is no such allowed vertex where four lines would meet. $\endgroup$
    – G. Smith
    Jun 19 '19 at 20:03

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