One way of deriving laws of energy, impulse and angular momentum of electromagnetic field conservation is following:

  1. Introduce two values below: $$ \mathbf P = \frac{c}{4 \pi}[\mathbf E \times \mathbf B], \quad W = \frac{1}{8 \pi}(\mathbf E^{2} + \mathbf B^{2}). $$

  2. Using Maxwell's equations and time derivative of these values, get the laws.

But how to argue an introduce of values from it. 1? Can Noether's theorem help to argue it?

  • $\begingroup$ These quantities are the symmetrized energy momentum tensor derived by the modification of Noether's argument which gives the correct linear momentum/angular-momentum relationship, but yes, in principle you use Noether's theorem. There was a similar question a few days ago in nonabelian gauge theory: physics.stackexchange.com/questions/31941/… . The simple answer is differentiate with respect to $g_{\mu\nu}$, but to fix the Noether prescription to get the same requires an elaborate discussion. $\endgroup$
    – Ron Maimon
    Commented Jul 19, 2012 at 2:45


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