"Modular invariance in math and physics"의 두 판 사이의 차이

2012년 10월 29일 (월) 11:37 판

path integral and moduli space of Riemann surfaces \[Z=\sum_{g=0}^{\infty} g_{s}^{-\chi(\Sigma_{g})}Z_{g}=\sum_{g=0}^{\infty} g_{s}^{2g-2}Z_{g}=\frac{1}{g_{s}^2}Z_{0}+g_{s}^{0}Z_{1}+g_{s}^2Z_{2}+\cdots\]
\(Z_{1}\) 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!
- compare with http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger_proper_time_formalism

@@ 12번째 줄: / 12번째 줄: @@
 ==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]] :<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}+\cdots</math><br>
 * <math>Z_{1}</math> is an integral over <math>M_1 = \mathbb{H}/SL(2,\mathbb{Z})</math> i.e. the fundamental domain.
 *  string theory (symmetries, modular group) has a natural covariant UV cutoff!<br>