"Renormalization"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 2번째 줄: | 2번째 줄: | ||
* way of pulling out sensible answers from Feynman diagrams that explode | * 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 | ** http://en.wikipedia.org/wiki/Effective_field_theory | ||
** effective ~ restricted to some interval | ** effective ~ restricted to some interval | ||
* easiest to grasp using functional integrals | * easiest to grasp using functional integrals | ||
| − | + | ||
| − | + | ||
| − | + | ||
==regularization== | ==regularization== | ||
| 20번째 줄: | 20번째 줄: | ||
* the values of observable quantities cannot depend on the way we've chosen to take the cutoff (regularize) | * 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 | * 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) | ** momentum regularization (modify the propagator by introducing cutoff dependent mass couplings) | ||
| − | ** lattice regulatization (replace R^d by a lattice, uses a small space cutoff) | + | ** lattice regulatization (replace $R^d$ by a lattice, uses a small space cutoff) |
** dimensional regularization | ** 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== | ==QED renormalization== | ||
| − | * [[QED renormalization]] | + | * [[QED renormalization]] |
| − | + | ||
| − | + | ||
==electroweak renormalization== | ==electroweak renormalization== | ||
| − | * | + | * spontaneous local [[spontaneous symmetry breaking|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== | ==books== | ||
| 60번째 줄: | 60번째 줄: | ||
* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
| − | + | ||
| + | ==expositions== | ||
| + | * Huang, Kerson. 2013. “A Critical History of Renormalization”. ArXiv e-print 1310.5533. http://arxiv.org/abs/1310.5533. | ||
| − | + | ||
==articles== | ==articles== | ||
2013년 10월 22일 (화) 02:04 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 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
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
expositions
- Huang, Kerson. 2013. “A Critical History of Renormalization”. ArXiv e-print 1310.5533. http://arxiv.org/abs/1310.5533.
articles
- Renormalization and quantum field theory R. E. Borcherds, 2010