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Qmechanic ♦
Qmechanic ♦
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Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$  ? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$ Thanks.

Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$  ? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$ Thanks.

Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$

I omitted the partial derivative bit
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Peter4075
Peter4075
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Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$ ? For example, can I write $$\frac{g_{\mu\nu}}{\partial x^{\mu}}$$$$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{g_{\phi\nu}}{\partial x^{\phi}},$$$$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{g_{\phi\nu}}{\partial\phi}?$$$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$ Thanks.

Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$ ? For example, can I write $$\frac{g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{g_{\phi\nu}}{\partial\phi}?$$ Thanks.

Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$ ? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$ Thanks.

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Peter4075
Peter4075
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Very simple index notation question

Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$ ? For example, can I write $$\frac{g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{g_{\phi\nu}}{\partial\phi}?$$ Thanks.