I've worked on this problem for forever and still don't really see the solution. Any help appreciated.

Say we have the Lagrangian for a scalar field that's $U(1)$ charged,$$\mathcal{L} ={1\over4}(F_{\mu\nu})^2 + |D_\mu\phi|^2 - M^2|\phi|^2,$$where $D_\mu = \partial_\mu - igA_\mu$ and $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. Calculate the conserved stress energy tensor that follows from invariance of $\mathcal{L}$ under spacetime translations.


closed as off-topic by ACuriousMind, Prahar, Kyle Kanos, Ali, Brandon Enright Oct 4 '14 at 16:25

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  • 4
    $\begingroup$ Do you know how to construct conserved quantities from symmetries of $\mathcal{L}$ using Noether's theorem? $\endgroup$ – Danu Oct 4 '14 at 12:31
  • $\begingroup$ Hi user60434. Welcome to Phys.SE. If you haven't already done so, please take a minute to read the definition of when to use the homework tag, and the Phys.SE policy for homework-like problems. $\endgroup$ – Qmechanic Oct 4 '14 at 13:46