Porter Johnson; 12 October 1999

This is an extension of some comments I made recently to the High School Physics Teachers in the

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:

You condense it with locusts and tape

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.