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## 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=[itex]\bar{ψ}[/itex]

Second one:

L=[itex]\bar{ψ}[/itex]

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?

I've seen two different answers to this question

First one:

L=[itex]\bar{ψ}[/itex]

_{e}(i∂-m_{e})[itex]ψ[/itex]_{e}+[itex]\bar{ψ}[/itex]_{p}(i∂-m_{p})[itex]ψ[/itex]_{p}-[itex]\frac{1}{4}[/itex]F^{μ}^{[itex]\nu[/itex]}F_{μ}_{[itex]\nu[/itex]}-e[itex]\bar{ψ}[/itex]_{e}γ^{μ}[itex]ψ[/itex]_{e}A_{μ}+e[itex]\bar{ψ}[/itex]_{p}γ^{μ}[itex]ψ[/itex]_{p}A_{μ}Second one:

L=[itex]\bar{ψ}[/itex]

_{e}(i∂-m_{e})[itex]ψ[/itex]_{e}+[itex]\bar{ψ}[/itex]_{p}(i∂-m_{p})[itex]ψ[/itex]_{p}-[itex]\frac{1}{4}[/itex]F^{μ}^{[itex]\nu[/itex]}F_{μ}_{[itex]\nu[/itex]}-g[itex]\bar{ψ}[/itex]_{e}γ^{μ}[itex]ψ[/itex]_{p}A_{μ}-h[itex]\bar{ψ}[/itex]_{p}γ^{μ}[itex]ψ[/itex]_{e}A_{μ}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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