I was adoubt if a symmetric stress-energy tensor 's lagrangian is symmetry .
Since {\cal L}= - \frac{1}{16\pi}F^{\mu\nu} F_{\mu\nu} is symmetry on \mu &\nu,the corresponding Stress-Energy Tensor \Theta^{\mu}\,_{\nu} = - \frac{1}{4 \pi} F^{\mu \alpha} \partial_{\nu}A_{\alpha} +...
Is the Lagrangian of the neutral Proca field
\mathcal{L}=-\frac{1}{16\pi}\left(F^{\mu\nu}F_{\mu\nu}-2m^2 A_{\mu} A^{\mu}\right)
symmetric?
And How to make sure whether it's symmetric.
Here are some pages of Arfken's “Mathematical Methods for Physicists ”
I don't How to work out the Green's function!
Can anyone explain (9.174)and(9.175) for me ?
I'm hoping for your help, Thank you !