# How do you derive the Lagrangian for the Standard Model?

Is there a way to derive the Lagrangian for the Standard Model just like one would for Einstein's field equations for instance? Also, how do you derive the Laganrigans for QCD and QED? Is it possible to do so from first principles?

In addition, what are these Lagrangians for these quantum field theories describing? An action?

Thanks,

• Comment to the question (v1): Most fundamental models are defined via their action/Lagrangian density (as opposed to their equations of motion). – Qmechanic Nov 13 '13 at 2:04
• Get yourself a whiteboard and marker and in a minute done! :) I like many of the minute physics videos, but the way he writes down the Lagrangian and says that's all there is to it! It sounds SOOO trite. (In fairness, he does come back and explain a bit more in later video, but this sounds awfully corny). – WetSavannaAnimal Nov 13 '13 at 11:30

It's not too hard to derive the Lagrangian for the electromagnetic field by staring at Maxwell's equations in the manifestly covariant form (i.e. in terms of the Maxwell Tensor $\partial_\alpha F^{\beta\,\alpha}=\mu_0 J^\beta$), and the geometric insights gained allowed people to generalize this action to non-Abelian theories like QCD.