# Interaction of photon+electron with parallel spins

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1. Apr 20, 2015

### jjustinn

As I understand it, the fundamental unit of interaction in QED is a term with a pair of (spinor) electron factors and a (vector) photon factor, represented in a Feynman diagram as two (anti-)electron lines and one photon line meeting at a vertex.

I get the case where the photon and electron have opposite spins: e.g. incoming electron, spin=+1/2, incoming photon, "spin"(helicity)=-1, outgoing electron, spin=-1/2.

But how do you handle incoming photon "spin"=+1, incoming electron spin=+1/2, outgoing electron spin=???

I can see how it would work with *four* lines -- i.e. topologically, the same as if there was no interaction at all (or an "X", rather than the three-line "Y" diagram)...but IIRC that's just not allowed (what would the term look like, with two vector and two spinor indices?)

At first, I thought that the interactions of photons/electrons with parallel spins just had to be a second-order effect (e.g. two Y diagrams back-to-back), but it seems like even in that case you would need to have an intermediate particle with spin=+3/2...but that's not available in QED.

What am I getting horribly wrong? I get the usual caveats, that Feynman diagrams only represent perturbative expansions etc etc...but even with those constraints, I'm sure that there's a way for this to work.

2. Apr 25, 2015