1. ### I Why does a Lagrangian matter for the standard model?

Hi, I don't know much about the standard model but I'm asking out of interest. Why do we actually need a Lagrangian for the standard model? Surely when you apply the relevant Euler-Lagrange equations, you end up with a variety of equations like the Maxwell equations or Dirac equations. Why...
2. ### I How to sum the first term in the Maxwell field Lagrangian

So the first term of the Lagrangian is proportional to ##{F_{\mu \nu}}{F^{\mu \nu}}##. I wrote out the matrices for ##{F_{\mu \nu}}## and ##{F^{\mu \nu}}## and multiplied at the terms together and added them up, but some of the terms didn't cancel like they should have. Should I have used minus...
3. ### Gauge invariance of lagrangian density

The problem: $$\mathcal{L} = F^{\mu \nu} F_{\mu \nu} + m^2 /2 \ A_{\mu} A^{\mu}$$ with: $$F_{\mu \nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$$ 1. Show that this lagrangian density is not gauge invariance 2.Derive the equations of motion, why is the Lorentzcondition still...

10. ### How does one derive the Lagrangian densities used in QFT?

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...