The successful unification of the electromagnetic and weak forces has led physicists to search for the possibility of also including the strong force in a unified scheme (a "grand unified theory") and even to contemplate the possibility of including gravity, thus unifying all the forces of Nature in a single "super force". However, much experimental and theoretical work is needed before such a goal is achieved.
New name for an old theory
Modern theories used today in the standard model of particle physics for
describing the interactions of particles are all gauge theories.
The term gauge relates to a particular feature of these theories, gauge
symmetry, viewed by many researchers as one of the most fundamental
features of physics. Yet as early as in the 1860s the Scotsman James Clerk
Maxwell formulated a theory of electromagnetism which in today's modern
terminology is a gauge theory. His theory, which still holds, united electricity
with magnetism and predicted, among other things, the existence of radio
waves.
We can illustrate the concept of gauge symmetry as
follows. Electric and magnetic fields can be expressed using potential
functions. These can be exchanged (gaugetransformed ) according
to a certain rule without changing the fields. The very simplest transformation
is to add a constant to the electrical potential. Physically this illustrates
the wellknown fact that electrical potential can be calculated from an
arbitrary zero point, since only the differences in potential are of significance.
This is why a squirrel can walk along a highvoltage cable without being
injured. That the zero point can be moved in this way is perceived by
physicists as a symmetry in the theory, gauge symmetry.
The order in which one performs two gauge transformations is immaterial.
We normally say that electromagnetism is an abelian gauge theory,
after the Norwegian mathematician Niels Henrik Abel, who lived between
1802 and 1829.
Quantum mechanics raises problems
Directly after quantum mechanics had been formulated around 1925 attempts
were made to unify the wave functions of quantum mechanics and the fields
of electromagnetism into a quantum field theory. But problems arose.
The new quantum electrodynamics became complicated and attempts
to perform calculations often gave unreasonable results. One reason was
that quantum theory predicts that the electromagnetic fields close to
e.g. an electron or a proton can spontaneously generate quantities of
very shortlived particles and antiparticles, virtual particles
.
A system of only one electron suddenly became a multiparticle problem!
The problem was solved in the 1940s by SinItiro Tomonaga, Julian Schwinger
and Richard P. Feynman (who shared the 1965 Nobel Prize in physics for
their contributions). The method developed by these three is called renormalization
and, simply expressed, means that individual particles can be viewed "somewhat
at a distance". In this way it is unnecessary to consider the virtual
particle pairs individually: the "cloud" of virtual particles
can be allowed to obscure the central, original particle. In this way,
the original particle gains a new charge and a new mass, among other things.
In modern terminology, Tomonaga, Schwinger and Feynman renormalized
an abelian gauge theory.
Quantum electrodynamics has been tested with greater
accuracy than any other theory in physics. Thus for example Hans Dehmelt
(Nobel Prize in Physics 1989) succeeded in measuring electron magnetism
in an ion trap with an accuracy of 12 digits. The first 10 digits agreed
directly with calculated results.
Unified electromagnetic and weak interaction
The discovery and study of radioactivity and the subsequent development
of atomic physics during the first half of the twentieth century produced
the concepts of strong and weak interaction. In simple terms strong
interaction holds the atomic nucleus together while weak interaction allows
certain nuclei to decay radioactively. As early as the 1930s a first quantum
field theory for weak interaction was formulated. This theory suffered
from problems that were even worse than those quantum electrodynamics
had had and not even the renormalization method of Tomonaga, Schwinger
and Feynman could solve them.
But in the mid1950s the researchers Chen Ning Yang and Robert L. Mills
found a first example of a quantum field theory with new features, a nonabelian
gauge theory. As opposed to the abelian variant, in which gauge transformations
can be performed in any order, the result of the nonabelian depends on
the order. This gives the theory a more complicated mathematical structure
but also opens up new possibilities. (A simple example of nonabelian
transformations is rotations in space. Try it yourself with a pencil,
as shown in
Figure 2b.)
The new possibilities of the theory were not fully exploited until the
1960s when a number of researchers collaborated in the development of
a nonabelian gauge theory that unites electromagnetism and weak interaction
into an electroweak interaction (Nobel Prize 1979 to Sheldon L.
Glashow, Abdus Salam and Steven Weinberg). This quantum field theory predicted
the new particles W and Z which were detected in 1983 at the European
CERN accelerator laboratory in Geneva (Nobel Prize 1984 to Carlo Rubbia
and Simon van der Meer).
History repeats itself
While the theory of electroweak interaction developed in the 1960s was
a great step forward, the research community at first found it difficult
to accept. When they tried to use the theory for calculating in more detail
the properties of the new W and Z particles (and many other physical quantities)
it gave unreasonable results. The situation resembled that of the 1930s
before Tomonaga, Schwinger and Feynman had succeeded in renormalizing
quantum electrodynamics. Many researchers were pessimistic about the possibilities
of going further with such a theory.
One person who had not given up hope of being able to renormalize nonabelian
gauge theories was Martinus J. G. Veltman.
With the help of Veltman's computer program 't Hooft's partial results
were now verified and together they worked out a calculation method in
detail. The nonabelian gauge theory of electroweak interaction had become
a functioning theoretic machinery and it was possible, just as it had
become for quantum electrodynamics 20 years previously, to start performing
precise calculations.
The theory's predictions verified
As described above, the theory of the electroweak force predicted the
existence of the new W and Z particles right from the start. But it was
only through 't Hooft's and Veltman's work that more precise prediction
of physical quantities involving properties of W and Z could start. Large
quantities of W and Z have recently been produced under controlled conditions
at the LEP accelerator at CERN. Comparisons between measurements and calculations
have all the time showed great agreement, thus supporting the theory's
predictions.
One particular quantity obtained with 't Hooft's and Veltman's calculation
method based on CERN results is the mass of the top quark, the
heavier of the two quarks included in the third family in the model. This
quark was observed directly for the first time in 1995 at the Fermilab
in the USA, but its mass had been predicted several years earlier. Here
too, agreement between experiment and theory was satisfactory.
When can we expect the next great discovery?
An important ingredient in the theory 't Hooft and Veltman have developed
is an as yet undemonstrated particle termed the Higgs particle (Fig. 1).
In the same way as other particles have been predicted by theoretical
arguments and later demonstrated experimentally, researchers are now awaiting
direct observation of the Higgs particle. Using calculations similar to
those of the mass of the top quark, there is a chance that one of the
existing accelerators can be persuaded to produce some Higgs particles.
But the only accelerator now under construction and powerful enough for
more detailed study of the new particle is the Large Hadron Collider
(LHC) at CERN. But researchers must contain themselves for a few years
to come since it is reckoned that the LHC will not be complete until 2005.

