"Gauge theory"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 18개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
| − | + | ==introduction== | |
| + | * {{수학노트|url=게이지_이론}} | ||
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| + | ==meaning of the gague invariance== | ||
* gauge = measure | * gauge = measure | ||
| 5번째 줄: | 9번째 줄: | ||
* Lagrangian should be gauge invariant. | * 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 | |
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| − | + | ==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> | ||
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| − | + | ==examples of renormalizable gauge theory== | |
| − | + | * [[QED]] | |
| − | + | * QCD | |
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| − | * [[QED]] | ||
| − | * QCD | ||
* [[renormalization]] | * [[renormalization]] | ||
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| − | + | ||
| − | + | ==Abelian gauge theory== | |
* abelian gauge theory has a duality | * abelian gauge theory has a duality | ||
| − | + | ||
| − | + | ||
| − | + | ==Non-Abelian gauge theory== | |
* [[Yang-Mills Theory(Non-Abelian gauge theory)|Yang-Mills Theory]] | * [[Yang-Mills Theory(Non-Abelian gauge theory)|Yang-Mills Theory]] | ||
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| − | + | ==differential geometry formulation== | |
| − | * | + | * manifold <math>\mathbb R^{1,3}</math> and having a vector bundle gives a connection |
| − | * connection <math>A</math> | + | * connection <math>A</math> = special kind of 1-form |
| − | * <math>dA</math> | + | * <math>dA</math> = 2-form which measures the electromagnetic charge |
| − | * Then the Chern class measures the magnetic charge. | + | * Then the Chern class measures the magnetic charge. |
| − | + | ||
| − | + | ||
| − | + | ==Principal G-bundle== | |
| − | * [[principal bundles]] | + | * [[principal bundles]] |
| − | * [[topology and vector bundles]] | + | * [[topology and vector bundles]] |
| − | + | ||
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| − | + | ==3d Chern-Simons theory== | |
| − | * 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 | + | * analogy with class field theory |
| − | * | + | * replace <math>\Sigma</math> by <math>spec O_K</math> |
| − | * then flat connection | + | * 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, | + | * 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] | + | * [http://www.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf] |
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| − | + | ==related items== | |
| − | * [[differential geometry and topology|differential geometry]] | + | * [[differential geometry and topology|differential geometry]] |
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| − | + | ||
| − | + | ==encyclopedia== | |
* http://en.wikipedia.org/wiki/principal_bundle | * http://en.wikipedia.org/wiki/principal_bundle | ||
* [http://en.wikipedia.org/wiki/Connection_%28vector_bundle%29 http://en.wikipedia.org/wiki/Connection_(vector_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 | * The Geometry of Physics: An Introduction | ||
| − | * An | + | * An elementary primer for gauge theory |
* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
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| − | * [http://www.math. | + | ==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]] | ||
| − | * [ | + | ==메타데이터== |
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q214850 Q214850] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'gauge'}, {'LEMMA': 'theory'}] | ||
| + | * [{'LOWER': 'gauge'}, {'LEMMA': 'symmetry'}] | ||
2021년 2월 17일 (수) 02:24 기준 최신판
introduction
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 \(F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \,\!\)
- general gauge fields tensor \(G_{\mu\nu}^{a}=\partial_{\mu}W_{\nu}^{a}-\partial_{\nu}W_{\mu}^{a}-gw^{abc}W_{\mu}^{b}W_{\nu}^{c}\)
examples of renormalizable gauge theory
- QED
- QCD
- renormalization
Abelian gauge theory
- abelian gauge theory has a duality
Non-Abelian gauge theory
differential geometry formulation
- manifold \(\mathbb R^{1,3}\) and having a vector bundle gives a connection
- connection \(A\) = special kind of 1-form
- \(dA\) = 2-form which measures the electromagnetic charge
- Then the Chern class measures the magnetic charge.
Principal G-bundle
3d Chern-Simons theory
- 3d Chern-Simons theory on \(\Sigma\times \mathbb R^{1}\) with gauge choice \(A_0=0\) is the moduli space of flat connections on \(\Sigma\).
- analogy with class field theory
- replace \(\Sigma\) by \(spec O_K\)
- then flat connection on \(spec O_K\) is given by Homomorphism group the absolute Galois group Gal(\barQ/K)->U(1)
- Now from An's article,
메모
encyclopedia
- http://en.wikipedia.org/wiki/principal_bundle
- http://en.wikipedia.org/wiki/Connection_(vector_bundle)
books
- The Geometry of Physics: An Introduction
- An elementary primer for gauge theory
- 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.
- On the Origins of Gauge Theory , Callum Quigley, April 14, 2003
- 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.
- Quantum field theory and the Jones polynomial Edward Witten, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399[1]
메타데이터
위키데이터
- ID : Q214850
Spacy 패턴 목록
- [{'LOWER': 'gauge'}, {'LEMMA': 'theory'}]
- [{'LOWER': 'gauge'}, {'LEMMA': 'symmetry'}]