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# index algebra context action free scalar field watch

1. I want to show that:

∂^uα(ϕ∗∂_uϕ)=∂_uα(ϕ ∗∂^uϕ)

where ∂_u = ∂/ ∂x^u, u running over the space-time i.e u=t,x,y,z
alpha and phi are functions of x

I'm unsure how to approach, since there I need to raise one index and lower the other, and they both have the same index, so I cant use something like what I usually would e.g g_{ab}x^{b}=x^{a} where g_{ab} is the metric tensor.

really stuck on this, any help greatly appreciated, many thanks.
2. (Original post by xfootiecrazeesarax)
I want to show that:

∂^uα(ϕ∗∂_uϕ)=∂_uα(ϕ ∗∂^uϕ)

where ∂_u = ∂/ ∂x^u, u running over the space-time i.e u=t,x,y,z
alpha and phi are functions of x

I'm unsure how to approach, since there I need to raise one index and lower the other, and they both have the same index, so I cant use something like what I usually would e.g g_{ab}x^{b}=x^{a} where g_{ab} is the metric tensor.

really stuck on this, any help greatly appreciated, many thanks.
Can you screen shot the question, as that's really difficult to read
3. (Original post by Slowbro93)
Can you screen shot the question, as that's really difficult to read
ps i caught a slowpoke today, on pokemon go, in my lecture theatre.
cp 351. however I'm about 25 whole candy away from evolving him into a slowbro
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4. (Original post by xfootiecrazeesarax)
ps i caught a slowpoke today, on pokemon go, in my lecture theatre.
cp 351. however I'm about 25 whole candy away from evolving him into a slowbro
dont worry, i've figured it.
(more importantly, caught one more slowpoke today )
5. (Original post by xfootiecrazeesarax)
dont worry, i've figured it.
(more importantly, caught one more slowpoke today )
Ooh, forgot to reply to this in the end Sorry!

What did you end up doing? I'm assuming you made use of covariant tensors?

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