- #1
JohnH
- 63
- 6
- TL;DR Summary
- Looking for a proof of
∂(∂L/∂[overline]Ψ[\overline])=0
and
∂L/∂Ψ=-[overline]Ψ[\overline]m
and
∂L/∂(∂[SUB]μ[/SUB]Ψ)=i[overline]Ψ[\overline]γ[SUP]μ[/SUP]
I'm having trouble following a proof of what happens when the Dirac Lagrangian is put into the Euler-Lagrange equation. This is the youtube video: and you can skip to 2:56 and pause to see all the math laid out. I understand the bird's eye results of the Dirac Lagrangian having an equation of motion that is either the Dirac equation or a [overline]Ψ[\overline] version of the Dirac equation, but I'm unclear about why, when putting the Dirac Lagrangian into the Euler-Lagrange equation, the following pieces are:
∂(∂L/∂[overline]Ψ[\overline])=0
and
∂L/∂Ψ=-[overline]Ψ[\overline]m
and
∂L/∂(∂μΨ)=i[overline]Ψ[\overline]γμ
Thanks for all replies.
∂(∂L/∂[overline]Ψ[\overline])=0
and
∂L/∂Ψ=-[overline]Ψ[\overline]m
and
∂L/∂(∂μΨ)=i[overline]Ψ[\overline]γμ
Thanks for all replies.