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index algebra context action free scalar field watch

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    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.
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    (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
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    (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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    (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 )
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    (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 :eek: Sorry!

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