"Modular invariance in math and physics"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* Is it useful? | * Is it useful? | ||
| 10번째 줄: | 10번째 줄: | ||
| − | ==path integral in string theory | + | ==path integral in string theory== |
* [[path integral and moduli space of Riemann surfaces]]<br><math>Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdtos</math><br> | * [[path integral and moduli space of Riemann surfaces]]<br><math>Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdtos</math><br> | ||
| 23번째 줄: | 23번째 줄: | ||
| − | ==circle method | + | ==circle method== |
| 31번째 줄: | 31번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[modular invariant partition functions|CFT on torus and modular invariant partition functions]] | * [[modular invariant partition functions|CFT on torus and modular invariant partition functions]] | ||
* [[Kac-Peterson modular S-matrix]] | * [[Kac-Peterson modular S-matrix]] | ||
* [[Hardy-Ramanujan tauberian theorem]] | * [[Hardy-Ramanujan tauberian theorem]] | ||
2012년 10월 28일 (일) 14:14 판
introduction
- Is it useful?
- Why is it important?
- Kac http://www.ams.org/publications/online-books/hmbrowder-hmbrowder-kac.pdf
- Modular invariance in lattice statistical mechanics http://aflb.ensmp.fr/AFLB-26j/aflb26jp287.pdf
path integral in string theory
- path integral and moduli space of Riemann surfaces
\(Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdtos\) - \(Z_{1}\) is an integral over \(M_1 = \mathbb{H}/SL(2,\mathbb{Z})\) i.e. the fundamental domain.
- string theory (symmetries, modular group) has a natural covariant UV cutoff!
circle method