Modular invariance in math and physics
http://bomber0.myid.net/ (토론)님의 2011년 10월 22일 (토) 07:30 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.
circle method