"Current algebra and anomalies in gauge field theory"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| + | ==internal algebra of symmetry== | ||
| + | * an internal symmetry is defined by the algebra of generators | ||
| + | $$ | ||
| + | [I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma} | ||
| + | $$ | ||
| + | * the generators, in turn, are given by the integral over the time-component of the currents | ||
| + | $$ | ||
| + | I_{\alpha}=\int d^3x J_{0,\alpha}(x) | ||
| + | $$ | ||
| + | * from these equations one obtains the equal-time commutation relation of the currents | ||
| + | $$ | ||
| + | [J_{0,\alpha}(\mathbf{x}),J_{0,\beta}(\mathbf{y})]=c_{\alpha \beta \gamma} J_{0,\alpha}(\mathbf{x})\delta(\mathbf{x}-\mathbf{y}) | ||
| + | $$ | ||
| + | |||
| + | * See [Pietschmann2011] and [[QCD and quarks]] for more | ||
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* [[QCD and quarks]] | * [[QCD and quarks]] | ||
* [[WZW (Wess-Zumino-Witten) model]] | * [[WZW (Wess-Zumino-Witten) model]] | ||
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* http://isites.harvard.edu/fs/docs/icb.topic1146666.files/IV-6-Anomalies.pdf | * http://isites.harvard.edu/fs/docs/icb.topic1146666.files/IV-6-Anomalies.pdf | ||
* Abel, [http://www.maths.dur.ac.uk/~dma0saa/lecture_notes.pdf Anomalies] | * Abel, [http://www.maths.dur.ac.uk/~dma0saa/lecture_notes.pdf Anomalies] | ||
| + | * [Pietschmann2011] Pietschmann, Herbert. “On the Early History of Current Algebra.” The European Physical Journal H 36, no. 1 (July 2011): 75–84. doi:10.1140/epjh/e2011-20013-0. | ||
2015년 3월 7일 (토) 03:43 판
internal algebra of symmetry
- an internal symmetry is defined by the algebra of generators
$$ [I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma} $$
- the generators, in turn, are given by the integral over the time-component of the currents
$$ I_{\alpha}=\int d^3x J_{0,\alpha}(x) $$
- from these equations one obtains the equal-time commutation relation of the currents
$$ [J_{0,\alpha}(\mathbf{x}),J_{0,\beta}(\mathbf{y})]=c_{\alpha \beta \gamma} J_{0,\alpha}(\mathbf{x})\delta(\mathbf{x}-\mathbf{y}) $$
- See [Pietschmann2011] and QCD and quarks for more
- QCD and quarks
- WZW (Wess-Zumino-Witten) model
- http://www.worldscientific.com/worldscibooks/10.1142/0131
- http://isites.harvard.edu/fs/docs/icb.topic1146666.files/IV-6-Anomalies.pdf
- Abel, Anomalies
- [Pietschmann2011] Pietschmann, Herbert. “On the Early History of Current Algebra.” The European Physical Journal H 36, no. 1 (July 2011): 75–84. doi:10.1140/epjh/e2011-20013-0.