@ACuriousMind dear moderator , I want some of my question to removed. I contacted stack exchange team many a times but no one responded. Can you help me with that and what is the way to do that
How come some sources have the Dirac Lagrangian with the derivative going both ways and some don't? The Lagrangian $\mathcal L=\bar\psi(i\gamma^\mu\partial_\mu-m)\psi $ gives the correct EOM's for $\psi^\dagger$ but not for $\psi$ because there's no derivative acting on $\psi^\dagger$?
as in if I calculate $\partial\mathcal L/\partial(\partial_\mu\phi^\dagger)$ I get zero
Some sources will write the partial derivative with a double ended arrow over it to indicate that we also take the derivative of the $\bar\psi$, but a lot don't
I am new to physics.stackexchange.com but not new to stackoverflow per se. I asked a question which I consider a Fermi problem:
In physics or engineering education, a Fermi problem [...] is an estimation problem designed to teach dimensional analysis or approximation of extreme scientific calcul...
$\psi$ is a four-component vector and the adjoint acts on this as a vector, the derivative doesn't live in this vector space so I'd say it's irrelevant and $\partial_{\mu}$ commutes with it