Undergrad Lorenz gauge, derivative of field tensor

[Lapidus]

F_μν = ∂_μA_ν- ∂_νA_μ

∂_μF_μν = ∂²_μA_ν - ∂_ν(∂_μA_μ) = ∂²_μA_νWhy ∂_ν(∂_μA_μ) and not ∂_μ∂_νA_μ ?

And why does ∂_ν(∂_μA_μ) drop out?

thank you

 

[phyzguy]

Because of the equality of mixed partial derivatives, \partial_\mu (\partial_\nu A_\mu) = \partial_\nu (\partial_\mu A_\mu). The Lorenz gauge assumes \partial_\mu A_\mu = 0, so that makes this term zero.