- #71

Ben Niehoff

Science Advisor

Gold Member

- 1,887

- 168

Ok. Then let me put it in this way:

[tex]{dp}{=}{R}{d}{\theta}[/tex]

[tex]{dq}{=}{R}{Sin}{(}{\theta}{)}{d}{\phi}[/tex]

That is not a coordinate transform.

It's actually worse than that! This statement:

[tex]dq = R \sin \theta \; d\phi[/tex]

is a lie! The right-hand side is not 'd' of anything, so it is incorrect to call this one-form 'dq'.

Remember that for any p-form [itex]\omega[/itex], we must have [itex]dd\omega = 0[/itex]. Taking 'd' of both sides of Anamitra's equation yields

[tex]\begin{align*} ddq &= R \; d ( \sin \theta \; d\phi) \\ 0 &= R \cos \theta \; d\theta \wedge d\phi \end{align*}[/tex]

which is clearly false.

Edit: I have deleted the rest of my post. It was a careful explanation of the issues Anamitra would face if he tried to follow the procedure he has outlined. I am offended, however, at the idea of doing his work for him.

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