"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이
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* looks like the coordinate invariance of gravity theory | * looks like the coordinate invariance of gravity theory | ||
* [[Gauge theory]] | * [[Gauge theory]] | ||
| − | * Usually, non-abelian gauge theory is called the YM theory. | + | * Usually, non-abelian gauge theory is called the YM theory. |
** QCD is one example. | ** QCD is one example. | ||
| 23번째 줄: | 23번째 줄: | ||
==original Yang-Mills model== | ==original Yang-Mills model== | ||
| − | * three kinds of photon | + | * three kinds of photon |
** one ordinary photon | ** one ordinary photon | ||
** two electrically charged photons with spin 1 which is physically impossible to exist | ** two electrically charged photons with spin 1 which is physically impossible to exist | ||
| − | * massless gauge fields | + | * massless gauge fields |
** for example, electromagnetic field(the only example at that time) | ** for example, electromagnetic field(the only example at that time) | ||
| 55번째 줄: | 55번째 줄: | ||
==Yang-Mills potential== | ==Yang-Mills potential== | ||
| − | * dual role | + | * dual role |
** a field in space-time | ** a field in space-time | ||
** operator in the isotopic-spin space | ** operator in the isotopic-spin space | ||
| 90번째 줄: | 90번째 줄: | ||
* [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 | ||
* [http://www.maths.ed.ac.uk/%7Ejmf/Teaching/EDC.html Electromagnetic duality for children] | * [http://www.maths.ed.ac.uk/%7Ejmf/Teaching/EDC.html Electromagnetic duality for children] | ||
| − | * [http://www.jstor.org/stable/2324574 What Is Geometry?] 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 | + | * [http://www.jstor.org/stable/2324574 What Is Geometry?] 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 |
* [http://cds.cern.ch/record/292286?ln=en Introduction to gauge theories and the Standard Model] CERN video lectures | * [http://cds.cern.ch/record/292286?ln=en Introduction to gauge theories and the Standard Model] CERN video lectures | ||
| 96번째 줄: | 96번째 줄: | ||
==articles== | ==articles== | ||
| − | * Huang, Teng. “Yang-Mills Connections on | + | * Huang, Teng. “Yang-Mills Connections on <math>G_{2}</math>-Manifolds and Calabi-Yau 3-Folds.” arXiv:1502.02090 [math-Ph], February 6, 2015. http://arxiv.org/abs/1502.02090. |
* [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry], Donaldson | * [http://www.ma.ic.ac.uk/%7Eskdona/YMILLS.PDF Yang-Mills Theory and Geometry], Donaldson | ||
* C. N. Yang and R. L. Mills, [http://dx.doi.org/10.1103/PhysRev.96.191 Conservation of Isotopic Spin and Isotopic Gauge Invariance], Phys. Rev. '''96''', 191 - 195 (1954) | * C. N. Yang and R. L. Mills, [http://dx.doi.org/10.1103/PhysRev.96.191 Conservation of Isotopic Spin and Isotopic Gauge Invariance], Phys. Rev. '''96''', 191 - 195 (1954) | ||
2020년 11월 13일 (금) 07:11 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
- 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
- Rivière, Tristan. “The Variations of Yang-Mills Lagrangian.” arXiv:1506.04554 [math], June 15, 2015. http://arxiv.org/abs/1506.04554.
- Slavnov, A. A. ‘New Approach to the Quantization of the Yang-Mills Field’. arXiv:1503.03380 [hep-Ph, Physics:hep-Th], 11 March 2015. http://arxiv.org/abs/1503.03380.
- 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
- 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
- Introduction to gauge theories and the Standard Model CERN video lectures
articles
- Huang, Teng. “Yang-Mills Connections on \(G_{2}\)-Manifolds and Calabi-Yau 3-Folds.” arXiv:1502.02090 [math-Ph], February 6, 2015. http://arxiv.org/abs/1502.02090.
- 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)