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

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==expository==
 
==expository==
 
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* 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.
 
* [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
 
* [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]
 
* [http://michaelnielsen.org/blog/?p=252 Introduction to Yang-Mills theories]

2015년 3월 12일 (목) 02:06 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