Renormalization

renormalization

• way of pulling out sensible answers from Feynman diagrams that explode
• there are two parts in the renormailization program
  
  • regularization - the divergences must be written down in some way so that they can be compared, added and subtracted
    
  • renormalization proper - the various divergences must be gathered together and extracted from the rest of the calculation
    

 

 

regularization

• root of the problem
  
  • probability of creating particles of colossal energies
    
  • in terms of Feynman diagrams, the momentum in a loop can run away to infinity
    
• dimensional regularization
  
  • regularization scheme (especially good in QCD)
    
  • regard the dimension as a continuous quantity
    
  • coupling constant changes accordingly as the dimension changes continuously
    
  • we get a new parameter called regularization scheme
    

 

 

QED renormalization

• three basic divergent diagrams and three counter-terms to match and three infinite constants
  
• electron self-energy diagram transforms the bare electron mass into the physical ones
  
• vertex diagram links bare electri charge to phstical electric charge
  
• photon self energy is related to the transformation of bare electric field strngth to physical field strength
  

 

 

books

• Renormalization: an introduction to renormalization, the renormalization John C. Collins
• 찾아볼 수학책
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

 

articles

•  
  Renormalization and quantum field theory
  
  • R. E. Borcherds
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://www.pdf-search.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/