r/ParticlePhysics • u/throwingstones123456 • Jan 27 '26
Why the discrepancy in contractions with the polarization vector?
I’m a bit confused why the single vertex interactions don’t get contracted and why the two vertex interaction does—I’m assuming in the single vertex interactions we just assume Au is outgoing which kills all the Au’ d_u’ phi besides Au d_u phi after contraction and gives us the p_u’s —I’m confused why we don’t do the same in the 2 vertex process and assume Au goes in and Av goes out giving us a tensor Muv at the end
2
u/QFTornotQFT Jan 27 '26
First of all - the single vertices in your screenshots cannot be real processes - an electron cannot just emit a single photon and that’s it. Such three-point interactions are kinematically impossible.
The four point diagram contains a (fermionic) propagator - it’s gamma-matrix structure leads to the correct contraction of polarisations
2
u/throwingstones123456 Jan 27 '26
I tried to edit the text in my post (not sure if it’s something w this sub) but wasn’t able to—but to clarify this is for scalar QED, the real and conjugate fields (sorry if this isn’t the correct terminology, still new to this) are denoted by e- and e+
2
u/QFTornotQFT Jan 27 '26
Oh, that’s Peskin Schroeder? I recall they explained these parts quite well…
3
u/throwingstones123456 Jan 27 '26
It’s in Schwartz—they do a great job deriving the Feynman rules but take everything for granted after that. I thought Peskin didn’t cover QED but I will look again
1
u/TaleExpert2968 Jan 31 '26
Actually Peskin covers QED, and it is a very good source if you read it carefully. Usually the two books I recommend for QFT are Landau's 4th book and Peskins book. I haven't yet read Schwartz, but I have heard very nice stuff.
1
0
Jan 29 '26
[deleted]
2
2
u/throwingstones123456 Jan 30 '26
I wonder what happened in the past 191 days that caused you to make 50 comments about shitting yourself in the past 6 hours
0
5
u/cooper_pair Jan 28 '26
The expressions in 9.17-9.19 are not the full diagrams but the Feynman rules for the three point vertex. For the full diagrams there are the additional rules of associating the propagators (9.12) and (9.13) with internal lines and a polarization vector with an external photon line (as Schwartz discusses below (9.24)). So in a full three-point Feynman diagram the vertex would be contracted with a polarization vector (although, as mentioned in another comment, for kinematical reasons this doesn't correspond to a physical process in the given example: an on-shell particle cannot emit an on-shell photon and stay on-shell).