Just out of curiosity, does anyone know why "renormalisation" is so named? Who first came up with the term, and why was it used? I did a mathematics undergraduate so to me "normalisation" means rescaling a Hilbert space vector to have unit norm.
Heuristically the term renormalisation makes some sense, as it is a systematic process for "normalising" divergent quantities to give well-defined probabilities. But it seems like a bad name to me, because it's patently impossible to truly "normalise" a divergent quantity. As far as I know, the correct perspective is that renormalisation replaces bare parameters by physical ones, thus removing the infinities.
Is there something I have misunderstood, or is that another case of historical contingency clouding the terminology. Surely "reparameterization" would be a better name?
Answer
Apparently, the term renormalization has been coined by several people in the 40's, as you can read on a CERN Courier from August, 2001 for instance. Below a quote of the relevant part:
The puzzle [how to tackle the infinities appearing on loop diagrams ?] was resolved in the late 1940s, mainly by Bethe, Feynman, Schwinger and Dyson. These famous theoreticians were able to show that all infinite contributions can be grouped into a few mathematical combinations, $Z_{i}$ (in QED, $i = 1,2$), that correspond to a change of normalization of quantum fields, ultimately resulting in a redefinition ("renormalization") of masses and coupling constants. Physically, this effect is a close analogue of a classical "dressing process" for a particle interacting with a surrounding medium.
but there is no reference to the original works. I guess they are the historical references introducing the full covariant perturbation theory, as you would have a good overview from the Nobel Prize website of Tomonaga, Schwinger and Feynman, or from the important paper by F.J. Dyson, The Radiation Theories of Tomonaga, Schwinger, and Feynman. Physical Review 75, 486–502 (1949).
As far as a conceive it, the name normalization has nothing really to do with norm, better with normal. You tend to make you're quantity normal (i.e. not wired or something, like a diverging physical quantity), you do not try to norm it.
More interesting is your second question, about a better name. This one already exists actually, and it is sometimes used: it's scaling invariance, scaling laws, or scaling something... This is cristal clear in the concept of renormalization group, from Wikipedia for instance, including all the historical relevant references, as for the CERN Courier cited above. For some reason the inventors of the renormalization group approach kept the name renormalization, but (re)scaling is definitely a better choice, as you rescale your theory actually (time-space length, mass, interaction constant, energy, ...)
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