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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?

asked Jan 27, 2016 in Theoretical Physics by Mephisto (15 points) [ revision history ]
edited Jan 28, 2016 by Mephisto

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