Timeline for MTW the contraction of a basis bi-vector with a basis two-form. Why am I getting this factor of 2?
Current License: CC BY-SA 4.0
13 events
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| Oct 22, 2020 at 7:14 | comment | added | pglpm | See also this answer to this similar question. | |
| Apr 10, 2020 at 20:18 | vote | accept | Steven Thomas Hatton | ||
| Mar 4, 2020 at 16:52 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
exercise 4.13 -> Exercise 4.12
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| Mar 4, 2020 at 16:51 | answer | added | Steven Thomas Hatton | timeline score: 0 | |
| Mar 4, 2020 at 7:35 | comment | added | Steven Thomas Hatton | P-forms are completely antisymmetric covariant tensors. P-multivectors are completely antisymmetric contravariant tensors. The contraction of one with the other is tensor contraction. The last equation in my question is the result of carefully following all the definitions given in exercise 4.12, which is the reference given for the result that I claim is wrong. | |
| Mar 4, 2020 at 7:09 | comment | added | Cinaed Simson | I recommend you edit the question and delete everything below "My question is:..." show us how you got the extra factor of $2$ in the first equation. Everything below your question is a distraction. Note, the inner product is in the sense that the $p$-vector is the dual to the $p$-covector. If you're using the tensor definition of the wedge product you'll get the wrong answer. The correct answer is $\left\langle \mathfrak{e}_{\alpha}\wedge\mathfrak{e}_{\beta},\mathbf{\omega}^{\mu}\wedge\mathbf{\omega}^{\nu}\right\rangle =\delta_{\alpha\beta}^{\mu\nu}$ as stated in MTW. | |
| Mar 4, 2020 at 1:47 | comment | added | Steven Thomas Hatton | I've thought about it. | |
| Mar 4, 2020 at 1:45 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
Added more justification for this being an error in MTW.
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| Mar 3, 2020 at 19:05 | comment | added | iSeeker | If no-one can provide a satisfactory answer, Steven, you might be a bit cheeky and try emailing Kip Thorne of MTW himself? There's a 2017 email address on iau.org/administration/membership/individual/3565 ; - > | |
| Mar 3, 2020 at 1:34 | comment | added | Steven Thomas Hatton | I'm going with "the book is wrong". I will explain in a posted answer. In the meantime, if anyone cares to preempt my folly with an answer showing the error of my ways, I would be grateful. My argument will be that the definitions given in Exercise 4.12 do not lead to the results stated in Box 4.1 and cited above. There is a missing $!p$. | |
| Feb 28, 2020 at 2:35 | review | Close votes | |||
| Mar 10, 2020 at 9:11 | |||||
| Feb 27, 2020 at 23:42 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
added a second example and erratum tag.
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| Feb 26, 2020 at 23:51 | history | asked | Steven Thomas Hatton | CC BY-SA 4.0 |