"Current algebra and anomalies in gauge field theory"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| (사용자 2명의 중간 판 6개는 보이지 않습니다) | |||
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==internal algebra of symmetry== | ==internal algebra of symmetry== | ||
* an internal symmetry is defined by the algebra of generators | * an internal symmetry is defined by the algebra of generators | ||
| − | + | :<math> | |
[I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma} | [I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma} | ||
| − | + | </math> | |
* the generators, in turn, are given by the integral over the time-component of the currents | * the generators, in turn, are given by the integral over the time-component of the currents | ||
| − | + | :<math> | |
I_{\alpha}=\int d^3x J_{0,\alpha}(x) | I_{\alpha}=\int d^3x J_{0,\alpha}(x) | ||
| − | + | </math> | |
* from these equations one obtains the equal-time commutation relation of the currents | * from these equations one obtains the equal-time commutation relation of the currents | ||
| − | + | :<math> | |
[J_{0,\alpha}(\mathbf{x}),J_{0,\beta}(\mathbf{y})]=c_{\alpha \beta \gamma} J_{0,\alpha}(\mathbf{x})\delta(\mathbf{x}-\mathbf{y}) | [J_{0,\alpha}(\mathbf{x}),J_{0,\beta}(\mathbf{y})]=c_{\alpha \beta \gamma} J_{0,\alpha}(\mathbf{x})\delta(\mathbf{x}-\mathbf{y}) | ||
| − | + | </math> | |
* See [Pietschmann2011] and [[QCD and quarks]] for more | * See [Pietschmann2011] and [[QCD and quarks]] for more | ||
| − | + | * [[Neutral pion decay]] | |
| − | + | ||
| 38번째 줄: | 38번째 줄: | ||
* Banerjee, H. ‘Chiral Anomalies In Field Theories’. arXiv:hep-th/9907162, 20 July 1999. http://arxiv.org/abs/hep-th/9907162. | * Banerjee, H. ‘Chiral Anomalies In Field Theories’. arXiv:hep-th/9907162, 20 July 1999. http://arxiv.org/abs/hep-th/9907162. | ||
* O’Raifeartaigh, L. ‘The Intertwining of Affine Kac–moody and Current Algebras’. International Journal of Modern Physics B 13, no. 24n25 (10 October 1999): 3009–20. doi:[http://dx.doi.org/10.1142/S0217979299002824 10.1142/S0217979299002824]. | * O’Raifeartaigh, L. ‘The Intertwining of Affine Kac–moody and Current Algebras’. International Journal of Modern Physics B 13, no. 24n25 (10 October 1999): 3009–20. doi:[http://dx.doi.org/10.1142/S0217979299002824 10.1142/S0217979299002824]. | ||
| + | * Holstein, Barry R. ‘Anomalies for Pedestrians’. American Journal of Physics 61, no. 2 (1 February 1993): 142–47. doi:10.1119/1.17328. | ||
* 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] | ||
| 45번째 줄: | 46번째 줄: | ||
* Sommerfield, Charles M. ‘Currents as Dynamical Variables’. Physical Review 176, no. 5 (25 December 1968): 2019–25. doi:10.1103/PhysRev.176.2019. | * Sommerfield, Charles M. ‘Currents as Dynamical Variables’. Physical Review 176, no. 5 (25 December 1968): 2019–25. doi:10.1103/PhysRev.176.2019. | ||
* Sugawara, Hirotaka. ‘A Field Theory of Currents’. Physical Review 170, no. 5 (25 June 1968): 1659–62. doi:10.1103/PhysRev.170.1659. | * Sugawara, Hirotaka. ‘A Field Theory of Currents’. Physical Review 170, no. 5 (25 June 1968): 1659–62. doi:10.1103/PhysRev.170.1659. | ||
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| + | [[분류:math and physics]] | ||
| + | [[분류:Lie theory]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q1454725 Q1454725] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'current'}, {'LEMMA': 'algebra'}] | ||
2021년 2월 17일 (수) 02:00 기준 최신판
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
encyclopedia
expositions
- Treiman, Sam, Roman Jackiw, and David J. Gross. Lectures on Current Algebra and Its Applications. Princeton University Press, 2015. http://www.worldscientific.com/worldscibooks/10.1142/0131
- [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.
- Weinberg, Steven. “Effective Field Theory, Past and Future.” arXiv:0908.1964 [gr-Qc, Physics:hep-Ph, Physics:hep-Th, Physics:physics], August 13, 2009. http://arxiv.org/abs/0908.1964.
- Adler, Stephen L. ‘Anomalies’. arXiv:hep-th/0411038, 2 November 2004. http://arxiv.org/abs/hep-th/0411038.
- Banerjee, H. ‘Chiral Anomalies In Field Theories’. arXiv:hep-th/9907162, 20 July 1999. http://arxiv.org/abs/hep-th/9907162.
- O’Raifeartaigh, L. ‘The Intertwining of Affine Kac–moody and Current Algebras’. International Journal of Modern Physics B 13, no. 24n25 (10 October 1999): 3009–20. doi:10.1142/S0217979299002824.
- Holstein, Barry R. ‘Anomalies for Pedestrians’. American Journal of Physics 61, no. 2 (1 February 1993): 142–47. doi:10.1119/1.17328.
- http://isites.harvard.edu/fs/docs/icb.topic1146666.files/IV-6-Anomalies.pdf
- Abel, Anomalies
articles
- Alekseev, Anton, and Thomas Strobl. “Current Algebras and Differential Geometry.” Journal of High Energy Physics 2005, no. 03 (March 15, 2005): 035–035. doi:10.1088/1126-6708/2005/03/035.
- Sommerfield, Charles M. ‘Currents as Dynamical Variables’. Physical Review 176, no. 5 (25 December 1968): 2019–25. doi:10.1103/PhysRev.176.2019.
- Sugawara, Hirotaka. ‘A Field Theory of Currents’. Physical Review 170, no. 5 (25 June 1968): 1659–62. doi:10.1103/PhysRev.170.1659.
메타데이터
위키데이터
- ID : Q1454725
Spacy 패턴 목록
- [{'LOWER': 'current'}, {'LEMMA': 'algebra'}]