[lordnacho]

There must be some smarter notation that captures the model with less verbosity?

Also, how on earth did various people put this together? Is there a good book about it?

[zbyszek]

There is; the equation on the CERN mug in the photo is an example. For example, the gluon Lagrangian (Section 1) may be more compactly written

-1/2 Tr F_{\mu\nu} F^{\mu\nu}

for a suitably defined F. Or further abbreviated to something like L_g.

It just depends on how much detail you need to expose.