Working on a Qft problem set I came across this small internal conflict, and I was wondering if any of you could help clear things up.

I constructed the energy-momentum tensor $$T_{\nu}^{\mu} = \frac{(\partial L)}{\partial(\partial_{\mu}A_{\lambda})}\partial_{\nu}A_{\lambda} - L\delta^{\mu}_{\nu}$$

And using the previous part's results to simplify I am left with $$T^{\mu\nu} = F^{\lambda\mu}\partial^{\mu}A_{\lambda}- L\delta^{\mu}_{\nu}$$

What is troubling me with this is how it is asymmetric across both $\mu$ and $\nu$. In a physical sense, how does this occur in reality? I'm pretty sure the math is done correctly.

Sorry for any errors I typed this up on my phone in econ.


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