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

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5번째 줄: 5번째 줄:
 
* 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.<br>
+
*  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<br>
+
*  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<br>
+
*  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<br>
+
*  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<br>
+
* [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 $G_{2}$-Manifolds and Calabi-Yau 3-Folds.” arXiv:1502.02090 [math-Ph], February 6, 2015. http://arxiv.org/abs/1502.02090.
+
* 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) 08:11 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

 

 

books

 

 

expository

   

articles

 

 

encyclopedia