"Renormalization"의 두 판 사이의 차이
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2012년 10월 29일 (월) 10:53 판
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
- regularization - the divergences must be written down in some way so that they can be compared, added and subtracted
- set of techniques used to understand a given quantum field theory in a certain energy or length interval
- http://en.wikipedia.org/wiki/Effective_field_theory
- effective ~ restricted to some 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
- probability of creating particles of colossal energies
- 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
- regularization scheme (especially good in QCD)
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
books
- Renormalization: an introduction to renormalization, the renormalization John C. Collins
- Kevin Costello, Renormalization and Effective Field Theory http://www.ams.org/bookstore-getitem/item=surv-170
- 찾아볼 수학책