- #1
MathematicalPhysicist
Gold Member
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I wanto show that:
[tex]\partial_{\mu} T^{\mu \nu}=0[/tex] for
[tex]T^{\mu\nu} = F^{\mu \rho}\eta_{\rho\sigma}F^{\sigma \nu}+\frac{1}{4}\eta^{\mu\nu}F_{\rho\sigma}F^{\rho\sigma})[/tex]
by using Maxwell's equations.
Here are my steps (it's not for HW, I am auditing this course):
[tex]\partial_{\mu} T^{\mu \nu} = F^{\mu \rho}_{,\mu} \eta_{\rho \sigma} F^{\sigma \nu} + F^{\mu \rho} \eta_{\rho \sigma} F^{\sigma \nu}_{,\mu} + \frac{1}{4} \eta^{\mu \nu} (F_{\rho \sigma , \mu} F^{\rho \sigma}+F_{\rho \sigma} F^{\rho \sigma}_{,\mu})[/tex]
I can't see the forrest from the trees, can someone hint me how to simplify this?
Thanks.
[tex]\partial_{\mu} T^{\mu \nu}=0[/tex] for
[tex]T^{\mu\nu} = F^{\mu \rho}\eta_{\rho\sigma}F^{\sigma \nu}+\frac{1}{4}\eta^{\mu\nu}F_{\rho\sigma}F^{\rho\sigma})[/tex]
by using Maxwell's equations.
Here are my steps (it's not for HW, I am auditing this course):
[tex]\partial_{\mu} T^{\mu \nu} = F^{\mu \rho}_{,\mu} \eta_{\rho \sigma} F^{\sigma \nu} + F^{\mu \rho} \eta_{\rho \sigma} F^{\sigma \nu}_{,\mu} + \frac{1}{4} \eta^{\mu \nu} (F_{\rho \sigma , \mu} F^{\rho \sigma}+F_{\rho \sigma} F^{\rho \sigma}_{,\mu})[/tex]
I can't see the forrest from the trees, can someone hint me how to simplify this?
Thanks.