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==expositions== | ==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.math.toronto.edu/%7Ecolliand/426_03/Papers03/C_Quigley.pdf On the Origins of Gauge Theory] , Callum Quigley, April 14, 2003 | ||
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* [http://www.math.cornell.edu/%7Egoldberg/Notes/AboutConnections.pdf WHAT IS A CONNECTION, AND WHAT IS IT GOOD FOR?] TIMOTHY E. GOLDBERG | * [http://www.math.cornell.edu/%7Egoldberg/Notes/AboutConnections.pdf WHAT IS A CONNECTION, AND WHAT IS IT GOOD FOR?] TIMOTHY E. GOLDBERG | ||
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==articles== | ==articles== | ||
2015년 12월 23일 (수) 00:15 판
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]