Timeline for Divergent Coulomb integrals in superfluid fluctuations
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| May 31, 2021 at 14:56 | vote | accept | SaMaSo | ||
| Jul 11, 2019 at 14:19 | comment | added | Lorenz Mayer | You are right. Of course there are IR divergencies in $d=1$. I added this part. | |
| Jul 11, 2019 at 14:18 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
included the case $d=1$.
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| Mar 1, 2019 at 21:12 | history | bounty ended | SaMaSo | ||
| Feb 28, 2019 at 11:54 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
added 15 characters in body
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| Feb 28, 2019 at 11:27 | comment | added | SaMaSo | I think Kardar's is different than dim regularization because his result does have IR divergencies for d=1,2. | |
| Feb 28, 2019 at 11:24 | comment | added | SaMaSo | Thanks, Lorenz. Could you please edit your answer reg UV divergencies, explicitly stating in d=2,3,4 the bound is not useful and for higher dimensions, the oscillations don't kill the integral and we need regularization? Then I can accept your answer. | |
| Feb 28, 2019 at 11:16 | comment | added | Lorenz Mayer | Kardar, i would assume, uses dimensional regularization from the beginning, even when no regularization is needed. Then you have to remember that dimensional regularizing an integral removes all but logarithmic divergencies. | |
| Feb 28, 2019 at 11:14 | comment | added | Lorenz Mayer | That is true. The oscillations will make a integral divergent whose integrand has some decay. | |
| Feb 28, 2019 at 11:12 | comment | added | SaMaSo | It still remains obscure how Kardar's approach is removing these divergencies all at once. But your answer has been really helpful | |
| Feb 28, 2019 at 11:10 | comment | added | SaMaSo | I see. So the initial bound that you were trying to improve wasn't a meaningful one for d=2,3,4. For higher dimensions, however, the integral is indeed UV divergent and needs regularization, and the intuition that the oscillations cancel each other doesn't really work. Is that correct? | |
| Feb 28, 2019 at 11:04 | comment | added | Lorenz Mayer | There are no UV divergences in the physically interesting cases of d=1,2,3,4. | |
| Feb 28, 2019 at 11:03 | comment | added | SaMaSo | This is getting perfect. So when you say "for all other d the integral is divergent and one has to introduce a regularization" I guess you mean UV divergence right? Then "So we see that there are no UV-divergencies really" is not accurate anymore. | |
| Feb 27, 2019 at 17:23 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
added 457 characters in body
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| Feb 27, 2019 at 16:55 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
added some comments on IR-divcergence in 2d
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| Feb 27, 2019 at 16:15 | comment | added | SaMaSo | Thanks for the edits. Nice note on alternating series. For the $d=2$ case, should we not recover a logarithmic potential? Also, $d=4$ case is interesting. I have to brush up my Bessel functions education:) Btw, do you have any ideas as for how to develop this calculation for higher dimensions? | |
| Feb 27, 2019 at 13:52 | history | undeleted | Lorenz Mayer | ||
| Feb 27, 2019 at 13:52 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
the previous version had a fatal mistake in its argument.
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| Feb 27, 2019 at 13:28 | history | deleted | Lorenz Mayer | via Vote | |
| Feb 27, 2019 at 13:25 | history | edited | Lorenz Mayer | CC BY-SA 4.0 |
added 3 characters in body
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| Feb 26, 2019 at 17:33 | comment | added | SaMaSo | Thank you for your answer. I think I'm not following when you introduce variable $u$. Should the integrand not be $(1-u^2)^{(d-3)/2} \, du$ instead? | |
| Feb 26, 2019 at 13:26 | history | answered | Lorenz Mayer | CC BY-SA 4.0 |