"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==
 
==internal algebra of symmetry==
 
* an internal symmetry is defined by the algebra of generators
 
* an internal symmetry is defined by the algebra of generators
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$$
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:<math>
 
[I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma}
 
[I_{\alpha},I_{\beta}]=c_{\alpha \beta \gamma}I_{\gamma}
−
$$
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</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
  
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* [[Neutral pion decay]]
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Chiral_anomaly
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* http://www.scholarpedia.org/article/Axial_anomaly
  
 
==related items==
 
==related items==
23번째 줄: 32번째 줄:
  
 
==expositions==
 
==expositions==
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* 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.
 
* [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.
 
* 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.
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* http://www.worldscientific.com/worldscibooks/10.1142/0131
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* Adler, Stephen L. ‘Anomalies’. arXiv:hep-th/0411038, 2 November 2004. http://arxiv.org/abs/hep-th/0411038.
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* Banerjee, H. ‘Chiral Anomalies In Field Theories’. arXiv:hep-th/9907162, 20 July 1999. http://arxiv.org/abs/hep-th/9907162.
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* 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].
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* 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]
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==articles==
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* 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.
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* Sommerfield, Charles M. ‘Currents as Dynamical Variables’. Physical Review 176, no. 5 (25 December 1968): 2019–25. doi:10.1103/PhysRev.176.2019.
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* 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]]
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[[분류:Lie theory]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q1454725 Q1454725]
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===Spacy 패턴 목록===
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* [{'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

\[ [J_{0,\alpha}(\mathbf{x}),J_{0,\beta}(\mathbf{y})]=c_{\alpha \beta \gamma} J_{0,\alpha}(\mathbf{x})\delta(\mathbf{x}-\mathbf{y}) \]




encyclopedia

related items


expositions

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

Spacy 패턴 목록

  • [{'LOWER': 'current'}, {'LEMMA': 'algebra'}]
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