"Free fermion"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 15개는 보이지 않습니다) | |||
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| − | + | ==introduction== | |
| − | * c=1/2 (for \psi real) | + | * <math>c=1/2</math> (for <math>\psi</math> real) |
| − | * c=1 (for \psi complex) | + | * <math>c=1</math> (for \psi complex) |
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| − | + | ==action== | |
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<math>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\,</math> | <math>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\,</math> | ||
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| − | + | ==OPE of fermionic fields== | |
| − | + | * <math>\psi(z)\psi(w) \sim \frac{1}{(z-w)}</math> | |
| − | + | * <math>\partial \psi(z) \psi(w) \sim -\frac{1}{(z-w)^2}</math> | |
| − | + | * <math>\partial \psi(z) \partial \psi(w) \sim -\frac{2}{(z-w)^3}</math> | |
| − | < | + | |
| + | ==energy-momentum tensor== | ||
* <math>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)</math> | * <math>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)</math> | ||
| + | * <math>T(z)\psi(w) \sim \frac{\psi(w)}{2(z-w)^2}+\frac{\partial \psi(w)}{(z-w)}</math> | ||
| + | * <math>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)}</math> | ||
| + | * <math>T(z)T(w) \sim \frac{1}{4(z-w)^4}+\frac{2T(w)}{(z-w)^2}+\frac{\partial T(w)}{(z-w)}</math> | ||
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| − | + | ==related items== | |
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* [[free massless boson]] | * [[free massless boson]] | ||
* [[Faddeev–Popov ghost fields|ghost fields]] | * [[Faddeev–Popov ghost fields|ghost fields]] | ||
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| − | + | ==computational resource== | |
| + | * 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 exercise 5] | ||
| − | + | [[분류:conformal field theory]] | |
| + | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
| − | * [ | + | ==메타데이터== |
| − | * [ | + | ===위키데이터=== |
| + | * ID : [https://www.wikidata.org/wiki/Q206604 Q206604] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LEMMA': 'zitterbewegung'}] | ||
| + | * [{'LOWER': 'trembling'}, {'LEMMA': 'motion'}] | ||
2021년 2월 17일 (수) 02:02 기준 최신판
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
expositions
메타데이터
위키데이터
- ID : Q206604
Spacy 패턴 목록
- [{'LEMMA': 'zitterbewegung'}]
- [{'LOWER': 'trembling'}, {'LEMMA': 'motion'}]