THE 1999 NOBEL PRIZE FOR PHYSICS goes to Gerardus 't Hooft of the University of Utrecht and Martinus Veltman, formerly of the University of Michigan and now retired, for their work toward deriving a unified framework for all the physical forces. Their efforts, part of a tradition going back to the nineteenth century, centers around the search for underlying similarities or symmetries among disparate phenomena, and the formulation of these relations in a complex but elegant mathematical language. A past example would be James Clerk Maxwell’s demonstration that electricity and magnetism are two aspects of a single electro-magnetic force.
Naturally this unification enterprise has met with various obstacles along the way. In this century quantum mechanics was combined with special relativity, resulting in quantum field theory. This theory successfully explained many phenomena, such as how particles could be created or annihilated or how unstable particles decay, but it also seemed to predict, nonsensically, that the likelihood for certain interactions could be infinitely large.
Richard Feynman, along with Julian Schwinger and Sin-Itiro Tomonaga, tamed these infinities by redefining the mass and charge of the electron in a process called renormalization. Their theory, quantum electrodynamics (QED), is the most precise theory known, and it serves as a prototype for other gauge theories (theories which show how forces arise from underlying symmetries), such as the electroweak theory, which assimilates the electromagnetic and weak nuclear forces into a single model.
But the electroweak model too was vulnerable to infinities and physicists were worried that the theory would be useless. Then ‘t Hooft and Veltman overcame the difficulty (and the anxiety) through a renormalization comparable to Feynman’s. To draw out the distinctiveness of Veltman’s and ‘t Hooft’s work further, one can say that they succeeded in renormalizing a non-Abelian gauge theory, whereas Feynman had renormalized an Abelian gauge theory (quantum electrodynamics). What does this mean? A mathematical function (such as the quantum field representing a particle’s whereabouts) is invariant under a transformation (such as a shift in the phase of the field) if it remains the same after the transformation. One can consider the effect of two such transformations, A and B. An Abelian theory is one in which the effect of applying A and then B is the same as applying B first and then A. A non-Abelian theory is one in which the order for applying A and B does make a difference. Getting the non-Abelian electroweak model to work was a formidable theoretical problem.
An essential ingredient in this scheme was the existence of another particle, the Higgs boson (named for Peter Higgs), whose role (in a behind-the-scenes capacity) is to confer mass upon many of the known particles. For example, interactions between the Higgs boson and the various force-carrying particles result in the W and Z bosons (carriers of the weak force) being massive (with masses of 80 and 91 GeV, respectively) but the photon (carrier of the electromagnetic force) remaining massless.
With Veltman’s and 't Hooft’s theoretical machinery in hand, physicists could more reliably estimate the masses of the W and Z, as well as produce at least a crude guide as to the likely mass of the top quark. (Mass estimates for exotic particles are of billion-dollar importance if Congress, say, is trying to decide whether or not to build an accelerator designed to discover that particle.) Happily, the W, Z, and top quark were subsequently created and detected in high energy collision experiments, and the Higgs boson is now itself an important quarry at places like Fermilab’s Tevatron and CERN’s Large Hadron Collider, under construction in Geneva.
For the text of the original researchers papers please see www.elsevier.nl/locate/npe.
(Recommended reading: 't Hooft, Scientific American, June 1980, excellent article on gauge theories in general; Veltman, Scientific American, November 1986, Higgs bosons. More information is available at the Swedish Academy website.