"Zamolodchikov's c-theorem"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==encyclopedia== * http://en.wikipedia.org/wiki/C-theorem) |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
| + | ==correlation functions== | ||
| + | * $\langle T(z,\bar{z})T(0,0) \rangle =\frac{F(|z|^2)}{z^4}$ | ||
| + | * $\langle \Theta(z,\bar{z})\Theta(0,0) \rangle =\frac{H(|z|^2)}{z^4}$ | ||
| + | * $\langle T(z,\bar{z})\Theta(0,0) \rangle =\langle \Theta(z,\bar{z})T(0,0) \rangle \frac{G(|z|^2)}{z^3\bar{z}}$ | ||
| + | ==C-function== | ||
| + | * $C=2F-G-\frac{3}{8}H$ | ||
| + | ===UV-limit=== | ||
| + | $$ | ||
| + | c=-\int_{0}^{\infty}dr \frac{2\dot{C}}{r}=\int_{0}^{\infty}dr \frac{3\dot{H}}{2r}=\frac{3}{2}\int_{0}^{\infty}dr r^3\langle \Theta(z,\bar{z})\Theta(0,0) \rangle | ||
| + | $$ | ||
==encyclopedia== | ==encyclopedia== | ||
* http://en.wikipedia.org/wiki/C-theorem | * http://en.wikipedia.org/wiki/C-theorem | ||
2013년 2월 25일 (월) 15:32 판
correlation functions
- $\langle T(z,\bar{z})T(0,0) \rangle =\frac{F(|z|^2)}{z^4}$
- $\langle \Theta(z,\bar{z})\Theta(0,0) \rangle =\frac{H(|z|^2)}{z^4}$
- $\langle T(z,\bar{z})\Theta(0,0) \rangle =\langle \Theta(z,\bar{z})T(0,0) \rangle \frac{G(|z|^2)}{z^3\bar{z}}$
C-function
- $C=2F-G-\frac{3}{8}H$
UV-limit
$$ c=-\int_{0}^{\infty}dr \frac{2\dot{C}}{r}=\int_{0}^{\infty}dr \frac{3\dot{H}}{2r}=\frac{3}{2}\int_{0}^{\infty}dr r^3\langle \Theta(z,\bar{z})\Theta(0,0) \rangle $$