Renormalization
imported>Pythagoras0님의 2012년 10월 28일 (일) 17:03 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
- 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 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
- http://en.wikipedia.org/wiki/Effective_field_theory
- effective ~ restricted to some interval
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
- 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
- probability of creating particles of colossal energies
- in terms of Feynman diagrams, the momentum in a loop can run away to infinity
- 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