Renormalization

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

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

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

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

Gerard t Hooft, Reflections on the renormalization procedure for gauge theories, arXiv:1604.06257 [hep-th], April 21 2016, http://arxiv.org/abs/1604.06257
Kasia Rejzner, Renormalization and periods in perturbative Algebraic Quantum Field Theory, http://arxiv.org/abs/1603.02748v1
http://arxiv.org/abs/1511.03180v1
Polyakov, A. M. ‘Kenneth Wilson in Moscow’. arXiv:1502.03502 [hep-Th, Physics:physics], 11 February 2015. http://arxiv.org/abs/1502.03502.
Guo, Li, Sylvie Paycha, and Bin Zhang. “Counting an Infinite Number of Points: A Testing Ground for Renormalization Methods.” arXiv:1501.00429 [math-Ph], January 2, 2015. http://arxiv.org/abs/1501.00429.
Panzer, Erik. “Renormalization, Hopf Algebras and Mellin Transforms.” arXiv:1407.4943 [hep-Th, Physics:math-Ph], July 18, 2014. http://arxiv.org/abs/1407.4943.
Huang, Kerson. 2013. “A Critical History of Renormalization”. ArXiv e-print 1310.5533. http://arxiv.org/abs/1310.5533.

Pawlowski, Jan M., Michael M. Scherer, Richard Schmidt, and Sebastian J. Wetzel. “Physics and the Choice of Regulators in Functional Renormalisation Group Flows.” arXiv:1512.03598 [cond-Mat, Physics:hep-Th], December 11, 2015. http://arxiv.org/abs/1512.03598.
Eröncel, Cem, and O. Teoman Turgut. ‘Exact Renormalization Group for Point Interactions’. arXiv:1412.8623 [hep-Th], 30 December 2014. http://arxiv.org/abs/1412.8623.
Renormalization and quantum field theory R. E. Borcherds, 2010