"Free fermion"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
| − | * c=1/2 (for \psi real) | + | * $c=1/2$ (for $\psi$ real) |
| − | * c=1 (for \psi complex) | + | * $c=1$ (for \psi complex) |
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==action== | ==action== | ||
| 16번째 줄: | 11번째 줄: | ||
| − | + | ==OPE of fermionic fields== | |
| − | + | * $\psi(z)\psi(w) \sim \frac{1}{(z-w)}$ | |
| − | + | * $\partial \psi(z) \psi(w) \sim -\frac{1}{(z-w)^2}$ | |
| − | + | * $\partial \psi(z) \partial \psi(w) \sim -\frac{2}{(z-w)^3}$ | |
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==energy-momentum tensor== | ==energy-momentum tensor== | ||
| + | * $T(z)=-\frac{1}{2}:\psi(z)\partial \psi(z):=-\frac{1}{2}\left(\lim_{w\to z}\psi(z)\partial \psi(z)+\frac{1}{(z-w)^2}\right)$ | ||
| + | * $T(z)\psi(w) \sim \frac{\psi(w)}{2(z-w)^2}+\frac{\partial \psi(w)}{(z-w)}$ | ||
| + | * $T(z)\partial \psi(w) \sim \frac{\psi(w)}{2(z-w)^3}+\frac{3\partial \psi(w)}{2(z-w)^2}+\frac{\partial^2 \psi(w)}{(z-w)}$ | ||
| + | * $T(z)T(w) \sim \frac{1}{4(z-w)^4}+\frac{2T(w)}{(z-w)^2}+\frac{\partial T(w)}{(z-w)}$ | ||
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==related items== | ==related items== | ||
| 40번째 줄: | 33번째 줄: | ||
* https://drive.google.com/file/d/0B8XXo8Tve1cxc0c0WC1Xb0l1MDg/view | * https://drive.google.com/file/d/0B8XXo8Tve1cxc0c0WC1Xb0l1MDg/view | ||
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| + | ==expositions== | ||
| + | * http://www.damtp.cam.ac.uk/user/j.laia/strings/StringSol2.pdf | ||
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[[분류:conformal field theory]] | [[분류:conformal field theory]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2016년 7월 21일 (목) 18:38 판
introduction
- $c=1/2$ (for $\psi$ real)
- $c=1$ (for \psi complex)
action
\(S= \int\!d^2x\, \psi^\dagger \gamma^0 \gamma^\mu \partial_\mu \psi= \int\!d^2z\, \psi^\dagger_R \bar\partial \psi_R + \psi_L^\dagger \bar\partial \psi_L\,\)
OPE of fermionic fields
- $\psi(z)\psi(w) \sim \frac{1}{(z-w)}$
- $\partial \psi(z) \psi(w) \sim -\frac{1}{(z-w)^2}$
- $\partial \psi(z) \partial \psi(w) \sim -\frac{2}{(z-w)^3}$
energy-momentum tensor
- $T(z)=-\frac{1}{2}:\psi(z)\partial \psi(z):=-\frac{1}{2}\left(\lim_{w\to z}\psi(z)\partial \psi(z)+\frac{1}{(z-w)^2}\right)$
- $T(z)\psi(w) \sim \frac{\psi(w)}{2(z-w)^2}+\frac{\partial \psi(w)}{(z-w)}$
- $T(z)\partial \psi(w) \sim \frac{\psi(w)}{2(z-w)^3}+\frac{3\partial \psi(w)}{2(z-w)^2}+\frac{\partial^2 \psi(w)}{(z-w)}$
- $T(z)T(w) \sim \frac{1}{4(z-w)^4}+\frac{2T(w)}{(z-w)^2}+\frac{\partial T(w)}{(z-w)}$
computational resource