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:
<μ+μ−|HI|γ>μ<γ|HI|e+e−>μ
The book says that the four elements <γ|HI|e+e−>μ are ∝(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?