Timeline for 3N-dimensional integral
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| May 17, 2020 at 18:27 | answer | added | chris | timeline score: 1 | |
| Jun 25, 2019 at 2:28 | answer | added | Carl Woll | timeline score: 6 | |
| Mar 19, 2013 at 4:30 | answer | added | Jens | timeline score: 12 | |
| Feb 21, 2013 at 4:32 | comment | added | acl | @LeonidShifrin good advice then, it should be described clearly there. | |
| Feb 20, 2013 at 2:33 | comment | added | Leonid Shifrin | @acl Also, when I referred to the dimensional regularization, I only meant that many textbooks which cover it describe the generalized spherical coordinates in some detail. I did not mean to suggest actually using the regularization, since the integral is convergent. | |
| Feb 20, 2013 at 2:33 | answer | added | whuber | timeline score: 12 | |
| Feb 20, 2013 at 2:31 | comment | added | acl | @LeonidShifrin right sorry, I somehow missed your second clarification (and yes I've also done far too many such integrals and didn't like them...) | |
| Feb 20, 2013 at 2:28 | comment | added | Leonid Shifrin | @acl I agree, I made a note on that myself, right below my first suggestion. I think this was just a reflex - I've done too many of those diagrams with dimensional regularization at the time (actually, I personally dislike it, because it is unphysical and regularizes both UV and IR, which is rather non-sensical given that UV and IR phenomena are often utterly different, except possibly for the case of anomalies. I prefer Pauli-Villars). But that's all in the past, now I am just a programmer, one of many. | |
| Feb 20, 2013 at 2:20 | comment | added | acl | @LeonidShifrin I'm fairly sure dimensional reguralization isn't necessary for multidimensional gaussian integrals :) It factorizes, also, you can go to generalized spherical coordinates. However this seems to really be asking "how do I set up multidimensional integrals". In any case I think the real answer is "you're better off with some sort of monte carlo scheme for large N and arbitrary integrands" | |
| Feb 20, 2013 at 0:09 | history | reopened |
whuber Mr.Wizard |
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| Feb 19, 2013 at 20:45 | review | Reopen votes | |||
| Feb 20, 2013 at 0:11 | |||||
| Feb 19, 2013 at 20:26 | comment | added | whuber | I have voted to reopen because I believe there is a legitimate interpretation of the question, as suggested by my edit of it (and I recall seeing similar issues raised on this site but do not recall seeing a general answer). | |
| Feb 19, 2013 at 20:19 | history | edited | whuber | CC BY-SA 3.0 |
added 159 characters in body; edited tags
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| Feb 18, 2013 at 16:29 | history | closed |
Ajasja Dr. belisarius rcollyer Yves Klett Vitaliy Kaurov |
not a real question | |
| Feb 18, 2013 at 16:17 | review | Close votes | |||
| S Feb 18, 2013 at 16:32 | |||||
| Feb 18, 2013 at 16:12 | review | First posts | |||
| S Feb 18, 2013 at 16:32 | |||||
| Feb 18, 2013 at 16:11 | comment | added | Leonid Shifrin | Actually, in this case, it is even much simpler, your integral factorizes into a product of simple integrals. | |
| Feb 18, 2013 at 16:04 | comment | added | Leonid Shifrin |
You don't need Mathematica to compute this. Switch to the generalized spherical coordinates and integrate over r and the angles. This is exmplained in many texts on Quantum Field Theory, look up dimensional regularization.
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| Feb 18, 2013 at 15:59 | comment | added | Szabolcs |
Integrate only supports integrating with respect to scalar variables, i.e. you need to integrate by the components of the vector. See the doc page on Integrate on how, and pay attention to spelling of names and capitalisation. (Integrate, E^x, and don't use N as a variable because it's a built-in symbol)
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| Feb 18, 2013 at 15:52 | history | asked | user5966 | CC BY-SA 3.0 |