# QED Interaction Lagrangian with two different fermions

## Main Question or Discussion Point

Let say I want to study electron-proton scattering (without considering proton's quarks, i.e. no QCD), which is the Lagrangian?

I've seen two different answers to this question

First one:
L=$\bar{ψ}$e(i∂-me)$ψ$e+$\bar{ψ}$p(i∂-mp)$ψ$p-$\frac{1}{4}$Fμ$\nu$Fμ$\nu$-e$\bar{ψ}$eγμ$ψ$eAμ+e$\bar{ψ}$pγμ$ψ$pAμ

Second one:
L=$\bar{ψ}$e(i∂-me)$ψ$e+$\bar{ψ}$p(i∂-mp)$ψ$p-$\frac{1}{4}$Fμ$\nu$Fμ$\nu$-g$\bar{ψ}$eγμ$ψ$pAμ-h$\bar{ψ}$pγμ$ψ$eAμ

with g,h some constants... (which constants? )

The difference is obviously the interaction part, both seem reasonable to me... but I've encountered both... So, which one is correct?

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## Answers and Replies

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dextercioby
Homework Helper
If the proton is assumed without internal structure, one can take the first option. The coupling is really done through the electric charge whose absolute value is the same for both particles. The g and h are probably meant to take into account the proton's internal structure through the so-called form factors.

Oops, i didn't see that the spinors were mixed. Sorry. See Bill's comment.

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Bill_K