Equations of motion from the Standard Model For some time now I have been wondering if you could not derive any sort of equations of motion from the Standard Model:
$$\mathscr{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+i\bar{\psi}D\psi+\bar{\psi}\phi\psi+h.c.+\vert D\phi\vert^2-V(\phi).$$
Since it is a Lagrangian shouldn't we be able to use the Euler-Lagrange equation to find some equations of motion? Since I don't understand the theory myself this might already have been done, or is being done by physicists. However that does not impact my curiosity. 
 A: Yes, it's a normal field theory, so you may derive the equations of motion. They will be the ordinary Maxwell's equations for the electromagnetic field
$$ \partial_\nu F^{\mu\nu} = j^\nu $$
with $j^\mu$ calculated as the sum of the conserved currents for the Dirac field and for the Higgs fields, combined with the Dirac equation coupled to the electromagnetic field (with some Yukawa interaction $y\cdot \phi\psi$ terms), and the Klein-Gordon equation for a charged scalar field with some $V'(\phi)$ and $\psi \psi$ terms added in the right hand side etc.
A: Yes, you can.  The Euler-Lagrange equations are found by minimizing the action with respect to small fluctuations in the fields.  For details look at the Relativistic Field Theory section of http://en.wikipedia.org/wiki/Classical_field_theory.  Note though that the resultant equations are usually not referred to as "equations of motion" since you are minimizing with respect to fields and not paths.
The minimization leads to many useful equations in QFT, for example the Klein-Gordon equation and the Dirac equation, depending on the Lagrangian.
