Renormalization

수학노트
Pythagoras0 (토론 | 기여)님의 2020년 11월 13일 (금) 18:27 판
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renormalization

  • way of pulling out sensible answers from Feynman diagrams that explode
  • there are two parts in the renormalization 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
  • set of techniques used to understand a given quantum field theory in a certain energy or length interval
  • easiest to grasp using functional integrals




regularization

  • the values of observable quantities cannot depend on the way we've chosen to take the cutoff (regularize)
  • introducing momentum or distance cutoff so as to render finite the large momentum or short distance limits of correlation functions
  • methods of regularization
    • momentum regularization (modify the propagator by introducing cutoff dependent mass couplings)
    • lattice regulatization (replace \(R^d\) by a lattice, uses a small space cutoff)
    • dimensional 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



electroweak renormalization

  • spontaneous local symmetry breaking or Higgs mechanism
  • mass term for gauge field is zero in the Lagranaian, but these bosons (W,Z bosons) have mass term. To resolve this, we employ Higgs mechanism



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