"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이
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| − | <h5> | + | <h5>books</h5> |
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994 | * Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994 | ||
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* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
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| − | <h5> | + | <h5>expository</h5> |
| − | * | + | * 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 | |
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| − | * http:// | + | * [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry]<br> |
| + | ** Donaldson | ||
| + | * [http://www.jstor.org/stable/2324574 What Is Geometry?]<br> | ||
| + | ** Shiing-Shen Chern, <cite style="line-height: 2em;">The American Mathematical Monthly</cite>, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686 | ||
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2011년 2월 3일 (목) 13:54 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.
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
quantization of Yang-Mills theory
We want to quantize this theory.
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
- 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
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