# Electron matrix element in a most simple QFT problem, the e+ e- annihilation

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In the beginning of PS book there is this short chapter called Invitation: Pair Production in $e^{+}$ $e^{-}$ Annihilation. The first non-zero term of the transition amplitude is:

$$<\mu^{+}\mu^{-}|H_{I}|\gamma>^{\mu}<\gamma|H_{I}|e^{+}e^{-}>_{\mu}$$

The book says that the four elements $<\gamma|H_{I}|e^{+}e^{-}>_{\mu}$ are $\propto (0,1,i,0)$

The electrons fly parallel to the $x$ axis (does the second coordinate accounts then for the total spin?). Now, my question:

What is that imaginary $i$ that appears in the third place? It is supposed to be a component in the $y$ axis (the collision happens in the $XZ$ plane). And what is the first coordinate ($0$)?

I had undergraduate QM long ago. That $i$ reminds me of things largely forgotten. It might have something to do with the spin of the electron or the polarization of the photon?

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