"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이
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| 67번째 줄: | 67번째 줄: | ||
* We want to quantize this theory. | * We want to quantize this theory. | ||
* standard model is a quantized version of a Yang-Mills theory of classical fields | * standard model is a quantized version of a Yang-Mills theory of classical fields | ||
| − | + | * [[mass gap in Yang-Mills theory]] | |
| 88번째 줄: | 88번째 줄: | ||
* http://michaelnielsen.org/blog/yang_mills.pdf | * 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] The Reference Frame | * [http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html History of Yang-Mills theory and wishful thinking] The Reference Frame | ||
| − | |||
* Overview of the links between the Langlands program and 4D super Yang-Mills | * 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 | * http://online.kitp.ucsb.edu/online/duallang_m10/frenkel/rm/flashtv.html | ||
2013년 4월 18일 (목) 10:36 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
- mass gap in Yang-Mills theory
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
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)