Gauge theory - 편집 역사

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imported>Pythagoras0: /* expositions */

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expositions

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articles

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@@ 147번째 줄: / 147번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q214850 Q214850]

← 이전 판		2020년 12월 27일 (일) 12:11 판
146번째 줄:		146번째 줄:
	[[분류:gauge theory]]		[[분류:gauge theory]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q214850 Q214850]

← 이전 판	2020년 11월 14일 (토) 00:21 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	* {{수학노트\|url=게이지_이론}}

	+
	+	==meaning of the gague invariance==
	+
	+	* gauge = measure
	+	* gauge invariance = measurement에 있어서의 invariance를 말함
	+	* Lagrangian should be gauge invariant.
	+
	+
	+
	+	===gauge symmetry and measurement===
	+
	+	* symmetry implies the existence of something unmeasurable.
	+	* phase is one example
	+
	+
	+
	+	==gauge field==
	+
	+	* a gauge field is defined as a four-vector field with the freedom of gauge transformation, and it corresponds to massless particlas of spin one
	+
	+	* one example is the electromagnetic field
	+
	+
	+
	+	==gauge field tensor==
	+
	+	* electromagnetic field tensor <math>F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \,\!</math>
	+	* general gauge fields tensor <math>G_{\mu\nu}^{a}=\partial_{\mu}W_{\nu}^{a}-\partial_{\nu}W_{\mu}^{a}-gw^{abc}W_{\mu}^{b}W_{\nu}^{c}</math>
	+
	+
	+
	+
	+
	+	==examples of renormalizable gauge theory==
	+
	+	* [[QED]]
	+	* QCD
	+	* [[renormalization]]
	+
	+
	+
	+
	+
	+	==Abelian gauge theory==
	+
	+	* abelian gauge theory has a duality
	+
	+
	+
	+
	+
	+	==Non-Abelian gauge theory==
	+
	+	* [[Yang-Mills Theory(Non-Abelian gauge theory)\|Yang-Mills Theory]]
	+
	+
	+
	+
	+
	+	==differential geometry formulation==
	+
	+	* manifold <math>\mathbb R^{1,3}</math> and having a vector bundle gives a connection
	+	* connection <math>A</math> = special kind of 1-form
	+	* <math>dA</math> = 2-form which measures the electromagnetic charge
	+	* Then the Chern class measures the magnetic charge.
	+
	+
	+
	+
	+
	+	==Principal G-bundle==
	+
	+	* [[principal bundles]]
	+	* [[topology and vector bundles]]
	+
	+
	+
	+
	+
	+
	+
	+	==3d Chern-Simons theory==
	+
	+	* 3d Chern-Simons theory on <math>\Sigma\times \mathbb R^{1}</math> with gauge choice <math>A_0=0</math> is the moduli space of flat connections on <math>\Sigma</math>.
	+	* analogy with class field theory
	+	* replace <math>\Sigma</math> by <math>spec O_K</math>
	+	* then flat connection on <math>spec O_K</math> is given by Homomorphism group the absolute Galois group Gal(\barQ/K)->U(1)
	+	* Now from An's article,
	+
	+
	+
	+
	+
	+	==메모==
	+
	+	* [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf]
	+	*
	+
	+
	+
	+
	+
	+	==related items==
	+
	+	* [[differential geometry and topology\|differential geometry]]
	+
	+
	+
	+
	+
	+	==encyclopedia==
	+
	+	* http://en.wikipedia.org/wiki/principal_bundle
	+	* [http://en.wikipedia.org/wiki/Connection_%28vector_bundle%29 http://en.wikipedia.org/wiki/Connection_(vector_bundle)]
	+
	+
	+
	+
	+
	+	==books==
	+
	+	* The Geometry of Physics: An Introduction
	+	* An elementary primer for gauge theory
	+	* [[2009년 books and articles\|찾아볼 수학책]]
	+
	+
	+
	+
	+
	+	==expositions==
	+	* Wilczek, Frank. “Unification of Force and Substance.” arXiv:1512.02094 [hep-Ph, Physics:hep-Th, Physics:physics], December 7, 2015. http://arxiv.org/abs/1512.02094.
	+	* [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf On the Origins of Gauge Theory] , Callum Quigley, April 14, 2003
	+
	+	* [http://www.thetangentbundle.net/papers/gauge.pdf Connections, Gauges and Field Theories]
	+
	+	* [http://www.math.cornell.edu/%7Egoldberg/Notes/AboutConnections.pdf WHAT IS A CONNECTION, AND WHAT IS IT GOOD FOR?] TIMOTHY E. GOLDBERG
	+
	+	==articles==
	+	* Slavnov, A. A. “60 Years of Gauge Fields.” arXiv:1511.05713 [hep-Th], November 18, 2015. http://arxiv.org/abs/1511.05713.
	+	* Weatherall, James Owen. ‘Fiber Bundles, Yang-Mills Theory, and General Relativity’. arXiv:1411.3281 [gr-Qc, Physics:hep-Th, Physics:math-Ph, Physics:physics], 12 November 2014. http://arxiv.org/abs/1411.3281.
	+	* [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial] Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[http://www.zentralblatt-math.org/zmath/en/ ]
	+	[[분류:math and physics]]
	+	[[분류:gauge theory]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 14일 (토) 00:21 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	* {{수학노트\|url=게이지_이론}}

−
−	~~==meaning of the gague invariance==~~
−
−	* gauge = measure
−	* gauge invariance = measurement에 있어서의 invariance를 말함
−	* Lagrangian should be gauge invariant.
−
−
−
−	~~===gauge symmetry and measurement===~~
−
−	* symmetry implies the existence of something unmeasurable.
−	* phase is one example
−
−
−
−	~~==gauge field==~~
−
−	* a gauge field is defined as a four-vector field with the freedom of gauge transformation, and it corresponds to massless particlas of spin one
−
−	* one example is the electromagnetic field
−
−
−
−	~~==gauge field tensor==~~
−
−	* electromagnetic field tensor <math>F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \,\!</math>
−	* general gauge fields tensor <math>G_{\mu\nu}^{a}=\partial_{\mu}W_{\nu}^{a}-\partial_{\nu}W_{\mu}^{a}-gw^{abc}W_{\mu}^{b}W_{\nu}^{c}</math>
−
−
−
−
−
−	~~==examples of renormalizable gauge theory==~~
−
−	* [[QED]]
−	* QCD
−	* [[renormalization]]
−
−
−
−
−
−	~~==Abelian gauge theory==~~
−
−	* abelian gauge theory has a duality
−
−
−
−
−
−	~~==Non-Abelian gauge theory==~~
−
−	* [[Yang-Mills Theory(Non-Abelian gauge theory)\|Yang-Mills Theory]]
−
−
−
−
−
−	~~==differential geometry formulation==~~
−
−	* manifold <math>\mathbb R^{1,3}</math> and having a vector bundle gives a connection
−	* connection <math>A</math> = special kind of 1-form
−	* <math>dA</math> = 2-form which measures the electromagnetic charge
−	* Then the Chern class measures the magnetic charge.
−
−
−
−
−
−	~~==Principal G-bundle==~~
−
−	* [[principal bundles]]
−	* [[topology and vector bundles]]
−
−
−
−
−
−
−
−	~~==3d Chern-Simons theory==~~
−
−	* 3d Chern-Simons theory on <math>\Sigma\times \mathbb R^{1}</math> with gauge choice <math>A_0=0</math> is the moduli space of flat connections on <math>\Sigma</math>.
−	* analogy with class field theory
−	* replace <math>\Sigma</math> by <math>spec O_K</math>
−	* then flat connection on <math>spec O_K</math> is given by Homomorphism group the absolute Galois group Gal(\barQ/K)->U(1)
−	* Now from An's article,
−
−
−
−
−
−	~~==메모==~~
−
−	* [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf]
−	*
−
−
−
−
−
−	~~==related items==~~
−
−	* [[differential geometry and topology\|differential geometry]]
−
−
−
−
−
−	~~==encyclopedia==~~
−
−	* http://en.wikipedia.org/wiki/principal_bundle
−	* [http://en.wikipedia.org/wiki/Connection_%28vector_bundle%29 http://en.wikipedia.org/wiki/Connection_(vector_bundle)]
−
−
−
−
−
−	~~==books==~~
−
−	* The Geometry of Physics: An Introduction
−	* An elementary primer for gauge theory
−	* [[2009년 books and articles\|찾아볼 수학책]]
−
−
−
−
−
−	~~==expositions==~~
−	* Wilczek, Frank. “Unification of Force and Substance.” arXiv:1512.02094 [hep-Ph, Physics:hep-Th, Physics:physics], December 7, 2015. http://arxiv.org/abs/1512.02094.
−	* [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf On the Origins of Gauge Theory] , Callum Quigley, April 14, 2003
−
−	* [http://www.thetangentbundle.net/papers/gauge.pdf Connections, Gauges and Field Theories]
−
−	* [http://www.math.cornell.edu/%7Egoldberg/Notes/AboutConnections.pdf WHAT IS A CONNECTION, AND WHAT IS IT GOOD FOR?] TIMOTHY E. GOLDBERG
−
−	~~==articles==~~
−	* Slavnov, A. A. “60 Years of Gauge Fields.” arXiv:1511.05713 [hep-Th], November 18, 2015. http://arxiv.org/abs/1511.05713.
−	* Weatherall, James Owen. ‘Fiber Bundles, Yang-Mills Theory, and General Relativity’. arXiv:1411.3281 [gr-Qc, Physics:hep-Th, Physics:math-Ph, Physics:physics], 12 November 2014. http://arxiv.org/abs/1411.3281.
−	* [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial] Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[http://www.zentralblatt-math.org/zmath/en/ ]
−	~~[[분류:math and physics]]~~
−	~~[[분류:gauge theory]]~~

@@ 132번째 줄: / 132번째 줄: @@
 ==expositions==
+* Wilczek, Frank. “Unification of Force and Substance.” arXiv:1512.02094 [hep-Ph, Physics:hep-Th, Physics:physics], December 7, 2015. http://arxiv.org/abs/1512.02094.
 * [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf On the Origins of Gauge Theory] , Callum Quigley, April 14, 2003
@@ 138번째 줄: / 138번째 줄: @@
 * [http://www.math.cornell.edu/%7Egoldberg/Notes/AboutConnections.pdf WHAT IS A CONNECTION, AND WHAT IS IT GOOD FOR?] TIMOTHY E. GOLDBERG
 ==articles==

← 이전 판	2020년 11월 16일 (월) 17:55 판
(차이 없음)

@@ 144번째 줄: / 144번째 줄: @@
 ==articles==
 * Weatherall, James Owen. ‘Fiber Bundles, Yang-Mills Theory, and General Relativity’. arXiv:1411.3281 [gr-Qc, Physics:hep-Th, Physics:math-Ph, Physics:physics], 12 November 2014. http://arxiv.org/abs/1411.3281.
 * [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial] Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[http://www.zentralblatt-math.org/zmath/en/ ]
 [[분류:math and physics]]
 [[분류:gauge theory]]

← 이전 판		2013년 4월 29일 (월) 20:53 판
141번째 줄:		141번째 줄:
	* [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial] Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[http://www.zentralblatt-math.org/zmath/en/ ]		* [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178138 Quantum field theory and the Jones polynomial] Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[http://www.zentralblatt-math.org/zmath/en/ ]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:gauge theory]]