"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* This is not a quantum theory. | * This is not a quantum theory. | ||
| 12번째 줄: | 12번째 줄: | ||
| − | ==basic concepts | + | ==basic concepts== |
* connection | * connection | ||
| 21번째 줄: | 21번째 줄: | ||
| − | ==original Yang-Mills model | + | ==original Yang-Mills model== |
* three kinds of photon<br> | * three kinds of photon<br> | ||
| 33번째 줄: | 33번째 줄: | ||
| − | ==weak force | + | ==weak force== |
| 41번째 줄: | 41번째 줄: | ||
| − | ==recipe | + | ==recipe== |
* prepare Dirac fields | * prepare Dirac fields | ||
| 53번째 줄: | 53번째 줄: | ||
| − | ==Yang-Mills potential | + | ==Yang-Mills potential== |
* dual role<br> | * dual role<br> | ||
| 63번째 줄: | 63번째 줄: | ||
| − | ==quantization of Yang-Mills theory | + | ==quantization of Yang-Mills theory== |
* We want to quantize this theory. | * We want to quantize this theory. | ||
| 72번째 줄: | 72번째 줄: | ||
| − | ==books | + | ==books== |
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994 | * Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994 | ||
| 85번째 줄: | 85번째 줄: | ||
| − | ==expository | + | ==expository== |
* [https://www.math.lsu.edu/%7Esengupta/papers/YMLisbon06Sengup.pdf 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 | ||
| 101번째 줄: | 101번째 줄: | ||
| − | ==articles | + | ==articles== |
* [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry]<br> | * [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry]<br> | ||
| 111번째 줄: | 111번째 줄: | ||
| − | ==encyclopedia | + | ==encyclopedia== |
* 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 | * http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory | ||
2012년 10월 28일 (일) 16:11 판
introduction
- This is not a quantum theory.
- This can be regarded as a generalization of theory of electromagetisms., 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”.
- Fifty years of Yang-Mills theory http://books.google.com/books?id=WV57GpYjYREC&pg=PA102&lpg=PA102&dq=weakly+interacting+boson+yang-mills&source=bl&ots=ztMiD8nOgz&sig=nhFiCtCQw2lAodU1zacqg3wueUQ&hl=ko&ei=W1jZTtuZCIqRiALR3c26BA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CHEQ6AEwCQ#v=onepage&q&f=false
- 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
- What Is Geometry? Shiing-Shen Chern, The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue (Oct., 1990), pp. 679-686
articles
- Yang-Mills Theory and Geometry
- Donaldson
- C. N. Yang and R. L. Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96, 191 - 195 (1954)