Interaction of photon+electron with parallel spins

[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.

 

[eljose79]

Thank you for your post. You are correct that in QED, the fundamental unit of interaction 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. However, there are several key points to consider when addressing your question.

Firstly, the spin of a particle in QED is not always conserved in interactions. This means that in certain interactions, the incoming and outgoing particles may have different spin states. This is allowed in QED as long as the total spin is conserved in the overall interaction.

Secondly, the term you mentioned with two vector and two spinor indices is not allowed in QED, as it would violate the conservation of electric charge. This is because the vector indices correspond to the electromagnetic field, which is associated with the electric charge of the particle.

Finally, when considering the case of an incoming photon with spin +1 and an incoming electron with spin +1/2, the outgoing electron can have any spin state as long as the total spin is conserved. This means that the outgoing electron could have spin +1/2, -1/2, or even 0. The key point is that the total spin state of the system must remain the same before and after the interaction.

In summary, the interaction you described is allowed in QED, as long as the total spin is conserved and the conservation of electric charge is satisfied. I hope this helps to clarify your understanding of QED. Keep asking questions and exploring the fascinating world of particle physics!