Timeline for How to perform this Gaussian matrix integral?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 7, 2022 at 1:41 | history | undeleted | Guoqing | ||
| Nov 7, 2022 at 1:40 | history | deleted | Guoqing | via Vote | |
| Nov 7, 2022 at 1:30 | history | edited | Guoqing | CC BY-SA 4.0 |
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| Nov 4, 2022 at 4:03 | comment | added | Guoqing | @TomDickens I've checked the Gaussian integral $\int \exp(-ax^2+bx)dx\propto \exp(b^2/4a)$, and I think it still holds for a Grassmann variable $b$. | |
| Nov 3, 2022 at 14:49 | comment | added | Tom Dickens | Are you using the fact that Grassmann variables anti-commute? | |
| Nov 3, 2022 at 14:17 | comment | added | Guoqing | @CarloBeenakker. I try to perform this integral by decomposing $dH$ into $dH_{11}dH_{12}\cdots dH_{NN}$, but I find it's not consistent with the answer in text book, even for integral over diagonal element $dH_{11}dH_{22}\cdots dH_{NN}$. Could you help me to check my derivations? | |
| Nov 3, 2022 at 14:14 | history | edited | Guoqing | CC BY-SA 4.0 |
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| Nov 3, 2022 at 0:04 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Nov 2, 2022 at 21:45 | comment | added | Tom Dickens | I do not have the book, but if it is like the lecture notes of the same name, published as arxiv.org/abs/hep-th/0410211, then just read the earlier sections on bosonic and Grassman integrals; he seems to explain the basics therein. | |
| Nov 2, 2022 at 16:39 | comment | added | Carlo Beenakker | the key reference is Efetov Supersymmetry in Disorder and Chaos --- this is quite sophisticated machinery, if you are unfamiliar with the basics I think you will first want to do some background reading. | |
| Nov 2, 2022 at 14:39 | history | asked | Guoqing | CC BY-SA 4.0 |