Renormalization for Philosophers by Butterfield and Bouatta in 2014
1. Introduction
2. Renormalization: the traditional approach
2.1 Prospectus: corrections needed
2.2 Renormalizing a coupling constant
- 2.2.1 Virtual particles and perturbation theory
2.3 The cut-off introduced
2.4 Letting the cut-off \[d\] go to zero
- 2.5.1 The physical rationale
- 2.5.2 A refined definition of renormalizability
2.6 Which theories are renormalizable?
3. The modern approach to renormalization
3.1 Good fortune explained: non-renormalizable terms dwindle at longer distances
- 3.1.1 Decoupling high-energy behaviour
- 3.1.2 Spacetime need not be a continuum
- 3.1.3 Effective theories only?
- 3.1.4 The renormalization group flow
3.2 Short-distance behaviour: the beta-function and asymptotic freedom
3.3 The perspective from the theory of condensed matter
- 3.3.1 Continuous phase transitions: scale-invariance
- 3.3.2 Critical exponents: the correlation length
- 3.3.3 Short distances: a natural lower limit
4. Nagelian reflections
4.1 Nagel endorsed
4.2 Renormalizability deduced at low energies as a family of Nagelian reductions
4.3 Universality as multiple realizability