"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이
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| 86번째 줄: | 86번째 줄: | ||
<h5>expository</h5> | <h5>expository</h5> | ||
| − | * Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects Ambar N. Sengupta | + | * [https://www.math.lsu.edu/%7Esengupta/papers/YMLisbon06Sengup.pdf Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects] Ambar N. Sengupta |
| − | * | + | * [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories] |
| + | * http://michaelnielsen.org/blog/yang_mills.pdf | ||
* [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking]<br> | * [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking]<br> | ||
** The Reference Frame | ** The Reference Frame | ||
| 112번째 줄: | 113번째 줄: | ||
* http://en.wikipedia.org/wiki/Yang-Mills_theory | * http://en.wikipedia.org/wiki/Yang-Mills_theory | ||
* http://en.wikipedia.org/wiki/Gauge_theory | * http://en.wikipedia.org/wiki/Gauge_theory | ||
| + | * http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory | ||
2011년 9월 23일 (금) 08:02 판
introduction
- This is not a quantum theory.
- This can be regarded as a generalization of electromagetics., i.e. bundle + connections
- looks like the coordinate invariance of gravity theory
- Gauge theory
- Usually, non-abelian gauge theory is called the YM theory.
- QCD is one example.
basic concepts
- connection
- curvature
original Yang-Mills model
- three kinds of photon
- one ordinary photon
- two electrically charged photons with spin 1 which is physically impossible to exist
- massless gauge fields
- for example, electromagnetic field(the only example at that time)
weak force
recipe
- prepare Dirac fields
- start with the free Dirac Lagrangian
- we demand the Lagrangian to be invariant under the SU(N) local gauge transformations
- structure constants are needed
- self-interaction of gauge fields starts to appear
Yang-Mills potential
- dual role
- a field in space-time
- operator in the isotopic-spin space
quantization of Yang-Mills theory
- We want to quantize this theory.
- standard model is a quantized version of a Yang-Mills theory of classical fields
books
- Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
- M. Nakahara “Geometry, Topology and Physics”.
- 찾아볼 수학책
- http://gigapedia.info/1/
- http://gigapedia.info/1/
expository
- Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects Ambar N. Sengupta
- Introduction to Yang-Mills theories
- http://michaelnielsen.org/blog/yang_mills.pdf
- History of Yang-Mills theory and wishful thinking
- The Reference Frame
- Overview of the links between the Langlands program and 4D super Yang-Mills
- http://online.kitp.ucsb.edu/online/duallang_m10/frenkel/rm/flashtv.html
- Electromagnetic duality for children
articles
- Yang-Mills Theory and Geometry
- Donaldson
- What Is Geometry?
- Shiing-Shen Chern, The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686
encyclopedia
- http://en.wikipedia.org/wiki/Yang-Mills_theory
- http://en.wikipedia.org/wiki/Gauge_theory
- http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory
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