Consider the interaction term $$\mathcal{L}_{\rm{int}}=-g\bar\psi_1\gamma_\mu\psi_1 \bar\psi_2\gamma^\mu\psi_2,$$ where $\psi_i$ are fermions. I would like to calculate the Feynman rule for the vertex.

Is it equal to $$-\left(i\right)g\gamma_\mu\gamma^\mu=-4ig,$$ or am I missing something about spinorial structure of the vertices?

  • $\begingroup$ @AccidentalFourierTransform, where do you get $2\times 2$ from? $\endgroup$ – Stig Oct 24 '18 at 14:29
  • $\begingroup$ @AccidentalFourierTransform shouldn't $\bar\psi_i$ and $\psi_i$ be distinguishable? $\endgroup$ – Stig Oct 24 '18 at 14:45
  • $\begingroup$ @AccidentalFourierTransform shouldn't we distinguish $\bar\psi_1$, $\psi_1$, $\bar\psi_2$ and $\psi_2$? Should we have 4 distinguishable particles? $\endgroup$ – Stig Oct 24 '18 at 15:22
  • 1
    $\begingroup$ More like $-i(\gamma_\mu)_{ab}(\gamma^\mu)_{cd}$ (no matrix multiplication). $\endgroup$ – AccidentalFourierTransform Oct 24 '18 at 15:24
  • 1
    $\begingroup$ @AccidentalFourierTransform by "no matrix multiplication" do you mean that $\gamma$s will be separately sandwiched between spinors? (And this separation prevents us to contract tensor indices) Sorry, this is the first time I see this kind of stuff $\endgroup$ – Vincenzo Ventriglia Oct 24 '18 at 15:42

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.