Thanks for your reply. Unfortunately, it is a little over my head. In particular, I had not heard of the Belinfante energy-momentum tensor until just now. I know how to derive the canonical energy-momentum tensor from the lagrangian density though. I am basically at the level where I can...
I'm trying to derive the conservaton of energy for electromagnetic fields with currents from the action principle, but I have some trouble understanding how the interaction term in the Lagrangian fits into this.
The approach I have seen so far has been to express the Lagrangian density as...