12 October 1999

The Royal Swedish Academy of
Sciences has awarded **the 1999 Nobel Prize in Physics**
jointly to

Professor **Gerardus 't Hooft**,
University of Utrecht, Utrecht, the Netherlands, and

Professor Emeritus **Martinus J. G. Veltman**, University of
Michigan, USA, resident in Bilthoven, the Netherlands.

*"for elucidating the quantum structure
of electroweak interactions in physics"*

This additional background material gives a short account of the discovery and its importance and is written mainly for physicists.

Particle physics deals with the properties
of the basic constituents of matter and the interactions between
them. Up to now, the most successful "language" in this branch of
physics has been that of relativistic quantum field theory. In
this framework elementary particles are represented by (second
quantized) fields, these being functions of space and time that
include creation and annihilation operators for particles. For
example light, the photon, is represented by such a field. These
fields are thus the building blocks of theories that attempt to
describe elementary particles and their interactions.

A highly successful theory of this kind is Quantum
Electrodynamics, commonly known as QED. QED describes, to a very
high degree of accuracy, the interactions of electrons, positrons
and light at low energies. It also enjoys a great deal of success
in many other applications, for example when it is used to
describe the interaction of light with atoms. However, the
development of QED and understanding its quantum structure did
not come easily but took several decades. The theory was to be
used perturbatively. In other words, taking into account higher
order corrections was expected to improve the accuracy of its
predictions. But instead some of these corrections were found to
be infinitely large. Many scientists contributed to elucidating
and solving the problems of QED, among them R. P. Feynman, J.
Schwinger and S.-I. Tomonaga who shared the 1965 Nobel Prize in
Physics for "their fundamental work in quantum electrodynamics,
with deep-ploughing consequences for the physics of elementary
particles". Through these heroic efforts QED became a predictive
theory. Employing perturbation theory, prescriptions were given
as to how to compute theoretical values of measurable quantities.
These could then be compared with experimental findings.
Pictorial diagrams, invented by Feynman and named after him,
helped a great deal in systematizing and facilitating the
theoretical computations. In this approach the previously
mentioned infinite quantum corrections appear in the diagrams as
closed loops. High precision measurements have established that
QED is an excellent theory.

The theory of weak interactions of elementary particles posed new
and even more challenging difficulties. These interactions play a
paramount role in nature. For example, the sun would not have
shone had there been no weak interactions. A relativistic quantum
field theory of weak interactions was proposed already in the
1930's by E. Fermi. This theory provided a great leap forward in
the understanding of weak interactions because it systematized
and described a large number of phenomena rather well. However,
it encountered two major problems. One was that in the framework
of perturbation theory, where it was to be used, quantum
corrections to the rate of any weak process were infinitely large
because of closed loops. Moreover, these infinities were far more
"vicious" than those encountered earlier in QED. The second
difficulty, referred to as the unitarity problem, was that the
theoretical expressions for cross sections, obtained even at the
lowest order of perturbation theory, looked absurd. At high
energies they violated the probability interpretation of quantum
mechanics. Furthermore, the methods developed earlier to cure the
problems encountered in QED were not applicable for solving the
difficulties of FermiÕs theory.

An attractive possibility was to modify Fermi's theory by
introducing two charged spin-one particles (charged vector bosons
also referred to as intermediate vector bosons). The theory did
then resemble QED, with the photon replaced by its massive
charged counterparts. There was an additional bonus as these
vector bosons could easily explain the observed
ÒuniversalityÓ of weak interactions. In spite of these
good features the above two problems persisted.

The great merit of this year's Laureates, Gerardus 't Hooft and
Martinus Veltman, is that they made a decisive contribution to
solving the difficulties inflicting theories of weak interactions
by investigating them in an extended framework called nonabelian
gauge theories or Yang-Mills theories, where the concept of
symmetry plays the leading role.

In 1954 C. N. Yang and R. L. Mills constructed the first example
of a nonabelian gauge theory. These physicists examined what
would happen if the isospin symmetry (introduced by W. Heisenberg
in 1932 in order to explain certain similarities of protons and
neutrons) were a "local", i.e., space-time dependent symmetry.
They discovered that such a requirement would entail the
existence of a trio of massless self-interacting vector bosons,
with electric charges +1, 0 and Ð1, in units of the proton
charge. In spite of the fact that no such massless particles
exist in nature, this way of thinking constituted the basis on
which the Standard Model of particle physics was built (see
below). The quantum structure of the "massless Yang-Mills theory"
was studied by several authors. Among those who at an early stage
made significant contributions in this domain were R. P. Feynman,
B. S. DeWitt, L. D. Faddeev and V. N. Popov.

At present the weak interactions are described, together with
electromagnetic interactions, by the Standard Electroweak Model
which is a nonabelian gauge theory appended by a QED-like
structure. In this Model there are three families of quarks and
leptons and four vector bosons. Two of the vector bosons carry
electric charge and are heavy (the W+ and the W- bosons), one is
heavy and neutral (the Z boson) and the fourth one is the photon.
The masses are introduced via the so-called Higgs mechanism. The
Model predicts the existence of a spin-zero particle, called the
Higgs Boson, which remains to be discovered. Furthermore,
FermiÕs theory emerges as the low-energy limit of the
Electroweak Model taking into account only interactions mediated
by the W+ and the W-bosons. In 1979 S. L. Glashow, A. Salam and
S. Weinberg received the Nobel Prize in Physics "for their
contributions to the theory of the unified weak and
electromagnetic interaction between elementary particles,
including, inter alia, the prediction of the weak neutral
current." The actual discovery of the massive vector bosons was
honored by the 1984 Nobel Prize in Physics to C. Rubbia and S.
van der Meer.

The contributions of 't Hooft and Veltman have had an enormous
impact on the development of particle physics. They showed that
the nonabelian quantum field theories could make sense and
provided a method for computing quantum corrections in
thesetheories. This was a pathbreaking discovery that made it
possible to compute quantum corrections to many processes and
compare the results with experimental observations or to make
predictions. For example, the mass of the top quark could be
predicted, using high precision data from the accelerator LEP
(Large Electron Positron) at the Laboratory CERN, Switzerland,
several years before it was discovered, in 1995 at the Fermi
National Laboratory in USA. The top quark, in spite of being too
heavy to be produced at the LEP accelerator, contributed through
quantum corrections by a measurable amount to several quantities
that could be measured at LEP. Similarly, comparison of
theoretical values of quantum corrections involving the Higgs
Boson with precision measurements at LEP gives information on the
mass of this as yet undiscovered particle.

By Professor Cecilia Jarlskog Member of the Nobel Committee for
Physics

References M. Veltman, Nuclear Physics B7 (1968) 637 G. 't Hooft,
Nuclear Physics B35 (1971) 167 G. 't Hooft and M. Veltman,
Nuclear Physics B44 (1972) 189; ibid. B50 (1972) 318.

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