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

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* http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory
 
* http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/Yang-Mills_theory
 
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2012년 10월 29일 (월) 10:56 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

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