Porter Johnson; 12 October 1999
The 1999 Nobel Prize in Physics was awarded to Tini Veltman and Gerard 't Hooft for proving that non-abelian gauge theories are renormalizable, using dimensional regularization. In these very intricate fundamental theories, " bare " or "undressed" particles [such as electrons and photons] are the fundamental entities of the theories as formulated, but one can observe only the "fully clothed" particles [real electrons are always enshrouded in photon clouds, and real photons are dressed in clouds of virtual electron-positron pairs]. Therefore, very elaborate procedures must be employed to obtain consistent results for observable quantities.
.The "dimensional regularization" concept involves formulating the theory and calculating quantities in "d" space-time dimensions, and carefully extirpating the unphysical parts in the limit d --->4. Why such an arcane approach? So that you don't spoil the gauge symmetries of theories by arbitrary procedures, such as introducing fictitious wrong-signature particles, putting in a space-time or 4-momentum cut-off, etc. Formulating the gauge theory on a lattice is also a sensible procedure, since one can impose and maintain a lattice version of the gauge symmetry; the only problem is to determine when one is seeing the continuous limit of the lattice theory, and not simply artefacts of the lattice.
The modern viewpoint is that renormalization is required in a quantum field theory for reasons that are physical, and one must do it whether it produces or involves a finite or infinite quantity. One may get a divergence whenever one calculate an unphysical quantity [that is, not measurable or preparable], but the divergences must cancel out of observable quantities. The issue is especially sensitive when massless particles are present.
Clear?? If not, consider the following venerable observation:
Still keeping on principal object in view---
To preserve its symmetrical shape
Fit the Fifth, The Hunting of the Snark,Lewis Carroll
Alfred Nobel [Swedish dynamite inventor and manufacturer] set up the physics prize in his will for a "device or discovery made by during the last year",but it seems to have more of a "lifetime achievement academy award".
Incidentally, one of Tini's students [a German friend of mine with the improbable but authentic name of Alfred Hill] was killed in PanAm Flight 192 over Lockerby Scotland several years ago.