"Yang-Mills Theory(Non-Abelian gauge theory)"의 두 판 사이의 차이

수학노트
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76번째 줄: 76번째 줄:
 
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
 
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
 
* M. Nakahara “Geometry, Topology and Physics”.
 
* 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
 
* [[2009년 books and articles|찾아볼 수학책]]
 
* [[2009년 books and articles|찾아볼 수학책]]
 
* http://gigapedia.info/1/
 
* http://gigapedia.info/1/
104번째 줄: 105번째 줄:
 
* [http://www.jstor.org/stable/2324574 What Is Geometry?]<br>
 
* [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
 
** 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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* 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)
  
 
 
 
 

2011년 12월 3일 (토) 10:02 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

 

 

expository

 

articles

 

 

encyclopedia

 

 

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