Timeline for What happens to the metric when we normalize the basis?
Current License: CC BY-SA 4.0
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| Nov 24, 2019 at 0:06 | comment | added | Michael Engelhardt | (revising my previous comment - I was being a bit too cautious) ... The notation in typical electrodynamics textbooks isn't very transparent with respect to the issues you're raising. Indeed, the hatted basis vectors are used, but the unhatted coordinates! If you replace also the unhatted coordinates with the hatted ones in the usual expression, then it seems to me things are consistent with your way of looking at it. | |
| Nov 23, 2019 at 23:19 | comment | added | Craig | Thank you so much! | |
| Nov 23, 2019 at 21:30 | comment | added | Craig | Thank you for clarifying this for me. I do have a follow up question if you have the time: in this answer (math.stackexchange.com/questions/618031/…) ∇ is derived for spherical coordinates. However in my case $\hat{∇}$ would have no pre-factors, since all of my dual vectors would be of length 1. This is not at all the usual ∇ operator found in, say electrodynamics textbooks, where that hatted cooridnate basis is certainly the one being used. | |
| Nov 23, 2019 at 21:24 | vote | accept | Craig | ||
| Nov 23, 2019 at 20:16 | history | edited | Michael Engelhardt | CC BY-SA 4.0 |
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| Nov 23, 2019 at 19:58 | history | edited | Michael Engelhardt | CC BY-SA 4.0 |
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| Nov 23, 2019 at 19:51 | history | answered | Michael Engelhardt | CC BY-SA 4.0 |