Let say I want to study electron-proton scattering (without considering proton's quarks, i.e. no QCD), which is the Lagrangian?(adsbygoogle = window.adsbygoogle || []).push({});

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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# QED Interaction Lagrangian with two different fermions

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