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

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<h5>introduction</h5>
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==introduction</h5>
  
 
* This is not a quantum theory.
 
* This is not a quantum theory.
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<h5>basic concepts</h5>
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==basic concepts</h5>
  
 
* connection
 
* connection
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<h5>original Yang-Mills model</h5>
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==original Yang-Mills model</h5>
  
 
*  three kinds of photon<br>
 
*  three kinds of photon<br>
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<h5>weak force</h5>
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==weak force</h5>
  
 
 
 
 
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<h5>recipe</h5>
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==recipe</h5>
  
 
* prepare Dirac fields
 
* prepare Dirac fields
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<h5>Yang-Mills potential</h5>
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==Yang-Mills potential</h5>
  
 
*  dual role<br>
 
*  dual role<br>
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<h5>quantization of Yang-Mills theory</h5>
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==quantization of Yang-Mills theory</h5>
  
 
* We want to quantize this theory.
 
* We want to quantize this theory.
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<h5>books</h5>
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==books</h5>
  
 
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
 
* Baez and Muniain (“Knots, Gauge Fields and Gravity”, World Scientific 1994
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<h5>expository</h5>
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==expository</h5>
  
 
* [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
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<h5>articles</h5>
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==articles</h5>
  
 
* [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>
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<h5>encyclopedia</h5>
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==encyclopedia</h5>
  
 
* 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) 14:07 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

 

 

==expository

 

 

==articles

 

 

==encyclopedia