- #1
lfqm
- 22
- 0
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]e(i∂-me)[itex]ψ[/itex]e+[itex]\bar{ψ}[/itex]p(i∂-mp)[itex]ψ[/itex]p-[itex]\frac{1}{4}[/itex]Fμ[itex]\nu[/itex]Fμ[itex]\nu[/itex]-e[itex]\bar{ψ}[/itex]eγμ[itex]ψ[/itex]eAμ+e[itex]\bar{ψ}[/itex]pγμ[itex]ψ[/itex]pAμ
Second one:
L=[itex]\bar{ψ}[/itex]e(i∂-me)[itex]ψ[/itex]e+[itex]\bar{ψ}[/itex]p(i∂-mp)[itex]ψ[/itex]p-[itex]\frac{1}{4}[/itex]Fμ[itex]\nu[/itex]Fμ[itex]\nu[/itex]-g[itex]\bar{ψ}[/itex]eγμ[itex]ψ[/itex]pAμ-h[itex]\bar{ψ}[/itex]pγμ[itex]ψ[/itex]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?
I've seen two different answers to this question
First one:
L=[itex]\bar{ψ}[/itex]e(i∂-me)[itex]ψ[/itex]e+[itex]\bar{ψ}[/itex]p(i∂-mp)[itex]ψ[/itex]p-[itex]\frac{1}{4}[/itex]Fμ[itex]\nu[/itex]Fμ[itex]\nu[/itex]-e[itex]\bar{ψ}[/itex]eγμ[itex]ψ[/itex]eAμ+e[itex]\bar{ψ}[/itex]pγμ[itex]ψ[/itex]pAμ
Second one:
L=[itex]\bar{ψ}[/itex]e(i∂-me)[itex]ψ[/itex]e+[itex]\bar{ψ}[/itex]p(i∂-mp)[itex]ψ[/itex]p-[itex]\frac{1}{4}[/itex]Fμ[itex]\nu[/itex]Fμ[itex]\nu[/itex]-g[itex]\bar{ψ}[/itex]eγμ[itex]ψ[/itex]pAμ-h[itex]\bar{ψ}[/itex]pγμ[itex]ψ[/itex]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?
Last edited: