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The Quantum Theory of Fields III: Supersymmetry

by Steven Weinberg, Cambridge University Press, ISBN 0 521 66000 9 (hbk £32.50/$49.95).

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The third volume in Steven Weinberg’s very successful collection on “The Quantum Theory of Fields” covers the topical area of supersymmetry and appears three years after the celebrated opening ones on “Foundations”(1995) and “Modern applications (1996). If these two volumes were considered masterpieces in a modern and original presentation of the basics of quantum field theory and its penetration in the recent development of particle physics, with the machinery of spontaneously broken gauge theories, the new volume embraces the wide subject of supersymmetry in Weinberg’s typical style, which always means a self contained treatment of the subject, from its foundations and motivations, to its most recent application as a possible scenario for new physics beyond the Standard Model (SM).

Weinberg’s main motivation for “Supersymmetry”as a quest for a unified theory relies on the possible solution of the so-called hierarchy problem, that is, the explanation of the “mystery” of the enormous ratio between the electroweak scale (around 300 GeV) and the Planck scale (1019GeV). It is worth noticing that such a fine-tuning problem, which calls for new physics at the TeV scale and is one of the main reasons for future searches at the LHC under construction at CERN, was raised by Weinberg himself in a famous paper with Eldad Gildener (1976 Phys. Rev.D13, 3333), and by two more of the main contributors to the modern theory of electroweak and strong interactions, Martinus Veltman (1981 Acta Phys. Polon.B12 437) and Luciano Maiani (1979 Proc. Summer School of Gif-sur-YvetteIN2P3 1).

Supersymmetry is the only known example of the enlargement of the space-time symmetry of physical laws (the so-called Poincaré symmetry based on Einstein’s special relativity), which is consistent with all axioms of relativistic quantum field theory. In so doing it unites particles of different spin, thus predicting a variety of new species when applied to the SM of the electroweak and strong interactions.

Weinberg’s exposition (in chapters 24-32) starts with a synthetic but complete presentation of the mathematical foundations of supersymmetry, called “graded Lie algebras”, which is a generalization of the concept, more familiar to physicists, of Lie algebras and continuous Lie groups (chapter 25).

As a preliminary to the above, he recalls in chapter 24, with an original presentation, the “no-go” theorems, which are the basis of the (failed) attempts, prior to supersymmetry, to unite space-time with internal symmetries (such as isospin or SU(3) eightfold way symmetries). He then undertakes, in chapter 26, supersymmetric field theories, using superfields, that is fields living in superspace, an abstract space that unifies space-time points with anticommuting coordinates, able to encompass multiplets of particles with different statistics and spin. In chapter 27, he develops the subject of supersymmetric gauge theories, which realize the remarkable marriage between the principle of local Yang-Mills symmetry with supersymmetry.

The way in which Weinberg exposes the subject, with all of its subtleties and technical details, is spectacular. He covers non renormalization theorems, supersymmetry breaking and extended supersymmetry with an original, clear and self-contained presentation. He then develops, in chapter 28, supersymmetric versions of the SM, covering most of the problems at the core of today’s search forsupersymmetry in particle physics, namely the scale of supersymmetry breaking, the minimal supersymmetric SM, possible baryon- and lepton-number violation and gauge-mediated supersymmetry breaking.

In the last four chapters, Weinberg develops more theoretical aspects of supersymmetric field theories, which are, however, tremendously important to the theoretical motivation of supersymmetry and its role in the formulation of quantum theories of gravity.

General aspects of supersymmetry beyond perturbation theory are touched on in chapter 29, with the modern developments of electric-magnetic duality. The latter allows us to give “exact results” for the low-energy action of certain supersymmetric field theories that exhibit a Coulomb phase for the Higgs field (the Seiberg-Witten solutions).

The following chapters are devoted to Feynman rules for supersymmetric field theories (chapter 30), an elegant presentation of supergravity theory (chapter 31) and its essential aspects, from the weak-field limit to local supersymmetry to all orders and the basic role of the gauge field predicted by supergravity, the spin-3/2 gravitino, in gravity-mediated supersymmetry-breaking scenarios.

The final chapter is devoted to supersymmetry in high space-time dimensions and the merging role of extended objects, called p- branes, in the description of modern gauge theories as coming from more general schemes such as higher-dimensional supergravities, M-theory and string theory.

The book also contains, at the end of each chapter, “problems” for the reader to exercise in the subject, even giving alternative proofs of derived results. In this respect the book, like the two preceding volumes, is well suited to graduate students in physics and applied mathematics as well as researchers who want to get acquainted with the fascinating subject of supersymmetry.

The author has achieved in a superb way the important task of producing a volume on supersymmetry, building a bridge between a formal development and its most important applications in particle physics, through a self-contained and very original sequence of subjects and topics.

To conclude this review, let us recall some indirect experimental signals, alluded to also in different parts of Weinberg’s book, indicating that supersymmetry is a plausible scenario for new physics beyond the SM:

* the non-observation of proton decay via a neutral pion and a positron, excluding a minimal Grand Unified Theory (GUT);
* the LEP precision measurements, incompatible with gauge-coupling unification for conventional minimal GUTs, but in reasonable agreement with minimal supersymmetric GUTs, with supersymmetry broken at the TeV scale;
* the large top Yukawa coupling, unusually large compared with all other quark and lepton couplings;
* the possible solution of the dark-matter problem with some of the natural supersymmetric particles (the neutralinos) as natural dark-matter candidates (WIMPs).

Although none of these facts is per se a compelling reason for supersymmetry and alternative explanations may be found, it is fair to say that they can all be interpreted in the context of a supersymmetric extension of the SM. Whatever the final theory for quantum gravity may be, supersymmetry remains a deep and non-trivial extension of our concept of space-time symmetries.

Brookhaven and China to join forces in research

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Representatives of the National Natural Science Foundation of China (NNSFC) visited Brookhaven on 23-25 February to learn more about the scientific programme of Brookhaven’s new RHIC heavy ion collider and to explore opportunities for increased collaboration. A possible upgrade to the STAR experiment, to extend its particle identification capability, was a major focus of the discussion. The delegation also visited the Lawrence Berkeley National Laboratory, and a joint symposium to discuss practical aspects of the STAR upgrade is planned for Beijing this fall. The visit culminated in the signing of an agreement to cultivate future interest and collaboration on the RHIC scientific programme between institutions supported by the NNSFC and Brookhaven.

Swedish accelerators take a look at the past

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The first cyclotron in Sweden was a small 80 cm device built in 1938 at the Nobel Institute in Stockholm and capable of accelerating deuterons to 7 MeV. After the Second World War, an ambitious new machine at Uppsala took energies into a new domain.

The 50th anniversary of accelerator-based research at Uppsala, on 8 December 1999, merited a jubilee symposium. Gunnar Tibell, Sven Kullander and Arne Johansson looked back, while Bo Höistad, Göran Possnert, Nils Olsson, Jörgen Carlsson and Curt Ekström surveyed the present scene and looked to the future.

The first two copies of a new book (in Swedish), relating half a century of accelerator-based activities in Uppsala and edited by Torsten Lindqvist, was handed to the vice-chancellor of the university, Bo Sundqvist, and to Helge Tyrén, former professor of high-energy physics.

In the early 1940s, Tyrén, a student of 1926 Nobel Chemistry Laureate Theodor Svedberg, had constructed a neutron generator for the production of radionuclides. In Svedberg’s discussions with the main customer of these radionuclides, gynaecology professor John Naeslund, plans emerged for a more powerful accelerator – a cyclotron – to increase the quantities of radioactive substances.

Naeslund’s wife knew Göteborg textile magnate Gustaf Werner, who was the richest person in Sweden at that time and known for his generosity. The firm Werner & Carlström offered to finance a cyclotron, and one of its research objectives was to see how synthetic fibres were affected by neutron irradiation.

From cyclotron to synchrocyclotron

In 1945 Tyrén visited cyclotron laboratories in the US. The original intention was to obtain drawings of a cyclotron with an energy of about 20 MeV for radioisotope production. However, during the visit he found that a new principle of accelerating particles to much higher energies had just been invented by E McMillan.

This principle of phase stability was tested and shown to work during the spring of 1946, while Tyrén was in Berkeley. The question was whether it was too early to implement this new idea in Uppsala. Tyrén managed to convince Svedberg that, instead of a cyclotron, a synchrocyclotron should be built, and Werner & Carlstroem had no objections. The instrument’s energy of 200 MeV was above the threshold energy for the production of the newly discovered pi meson. Protons of this energy also have a sufficiently short wavelength to interact with individual nucleons in the nucleus, and the range in tissue is 25 cm, which is important for proton therapy.

On 8 December 1949, Crown Prince Gustaf Adolf inaugurated the Gustaf Werner Institute for Nuclear Chemistry (GWI). Exactly two years later, on 9 December 1951, Ernest O Lawrence, the inventor of the cyclotron, pressed the button to initiate the first beam circulating in the new synchrocyclotron.

For a few years, scientists in Uppsala could access protons of the highest energy in Western Europe. Several foreign physicists visited to familiarize themselves with these high-energy projectiles.

Meanwhile, CERN was founded and construction began for its first two accelerators: the synchrocyclotron (SC) and the proton synchrotron (PS). A large percentage of the Uppsala staff were recruited to take part in the build up of CERN’s new European laboratory. The Uppsala group, under Bengt Hedin, was responsible for the construction of the SC magnet.

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A spectrum of research

A milestone in the development of the GWI was the extraction of the proton beam in 1955, giving more flexibility to the arrangement of nuclear physics experiments. Nuclear spectroscopy was always an important part of the research, both off line and on line. Among the intermediate-energy physics experiments were the first studies of quasi-free proton-proton reactions, and later studies of pion production on atomic nuclei – so-called sub threshold reactions.

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Biomedical research began under the leadership of Börje Larsson, who was later to become professor of radiobiology. He was one of the pioneers in the history of radiosurgery, as well as in other therapeutic and diagnostic uses of the proton beam at the GWI. On 23 November 1957, in a pioneer proton irradiation of a malignant human cancer, he and physician Stig Stensson irradiated a woman suffering from a large malignant tumour of the uterus. In 1958 Boerje Larsson also participated, together with medical doctors Lars Leksell and Bror Rexed, in the first neurosurgery on patients.

For well over two decades, a large number of physics and biomedical research projects were carried out at the Uppsala machine. In 1977 it was closed for a major overhaul and also modification into a sector-focusing synchrocyclotron. It was reopened in 1986, with much improved performance. The energy can be varied in the 20-190 MeV range for protons, and a variety of different ions can be accelerated.

From ICE to CELSIUS

As well as providing beams for physics and biomedical research, the cyclotron is an injector for the cooler storage ring CELSIUS (Cooling with Electrons and Storing of Ions from the Uppsala Synchro-cyclotron). The CELSIUS proton energy can be raised to well over 1 GeV, making a new field of research available to the physicists.

CELSIUS uses the lattice magnets of the Initial Cooling Experiment (ICE), which was built at CERN in the late 1970s. The decision to send the equipment to Sweden was taken by CERN Council in December 1982, and additional funding for the ring was included in the 1983/4 budget of the Swedish Ministry of Education.

Ongoing work to improve the machine and extend laboratory space was accelerated so that the “new” ring could be accommodated. In the summer of 1983, 20 trucks transported the 40 magnets and 4 coils from Geneva to Uppsala. The experience acquired in building the ICE ring was of value to the CELSIUS project, and in particular the contributions by CERN’s Heiner Herr and Alfredo Susini should be mentioned. The first CELSIUS proton beam circulated in 1988.

The GWI ceased to exist in 1986, when it, together with the Tandem Accelerator Laboratory, formed a new national laboratory – the The Svedberg Laboratory (“The” is an abbreviation of Theodor), and a new university department, the Department of Radiation Sciences, with units in high-energy physics, nuclear physics, ion physics and physical biology.

Today around 300 physicists and medical researchers, from Sweden and abroad, use the two The Svedberg Laboratory accelerators. The Programme Advisory Committee can only accept a fraction of the proposed experiments. Notable experiments are those performed by two large collaborations – WASA and CHICSi, both at CELSIUS, and operating with light and heavy ions, respectively. The storage ring has two internal target stations – one for a gas jet target and one for pellets of frozen hydrogen or deuterium. Among the SC projects, international teams are using a neutron beam for both fundamental and applied research.

CERN contributions

Scientists from the GWI, and since 1986 from the Department of Radiation Sciences, have been very active in research at CERN. At the end of the 1960s, accelerator physicists contributed to the improvement of the SC, where experiments were initiated by an Uppsala group in 1967. Later SC experiments were carried out on pi mesic atoms and muon-induced fission.

At CERN’s LEAR antiproton ring, the production of heavy hypernuclei and lambda-antilambda pairs were studied. Pion-helium and proton-helium interactions were studied at the PS between 1967 and 1976. In 1977 the Uppsala group took part in one of the first experiments at the SPS proton synchrotron: hadron-hydrogen elastic scattering in the Coulomb interference region.

Since 1980 the group has collaborated in studies using CERN’s high-energy muon beam for the determination of polarized and unpolarized structure functions from nucleons and nuclei. A significant contribution to the build-up of the RICH detectors for the Delphi experiment at LEP has been made, as well as the running and analysis of Delphi. For the future LHC collider, the Uppsala group contributes to the semiconductor tracker for the ATLAS collaboration.

Dynamics of Heavy Electrons

by Y Kuramoto and Y Kitaoka, Oxford University Press, ISBN 0 19 851767 X (hbk £75)

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In this context “heavy electrons” means electrons in rare-earth and actinide metals that acquire very large effective masses owing to strong local correlations.

Introductory Statistical Mechanics

by Roger Bowley and Mariana Sanchez, Oxford University Press (2nd edn), ISBN 0 19 8505760 (pbk, £21.99).

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This text offers an introduction to the theory of condensed matter and first appeared in 1996. This edition includes three additional chapters on phase transitions and more examples.

Dynamics and Relativity 

by W D McComb, Oxford University Press, ISBN 0 19 850112 9 (pbk).

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This a comprehensive textbook sets out to introduce special relativity to mathematicians, mathematical physicists and physicists in a natural way and avoid all “gee-whizz”. There are ample exercises and an introduction to general relativity.

Defect and Microstructure Analysis by Diffraction

by R Snyder, J Fiala and H J Bunge, Oxford Science Publications, ISBN 0 19 850189 7 (£95, 780 pages).

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In the International Union of Crystallography series of monographs, this comprehensive compilation of 31 chapters from different authors looks at the latest developments in X-ray diffraction techniques.

Particle Astrophysics

by H V Klapdor-Kleingrothaus and K Zuber, revised edition, Institute of Physics Publishing, ISBN 0 75 030549 5 (pbk £34.99/$59.99, 470 pages).

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This is a revised and updated edition, in paperback, of a book that, when it first appeared a few years ago (Bookshelf, Summer 1998), merited the comment “more than just a graduate level textbook…it is also a sign of the times”.

Quantum Processes in Semiconductors

by B K Ridley, Oxford Science Publications (4th edn), ISBN 0 19 850580 9 (pbk £27.50 435 pages).

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First published in 1982, this work provides a useful overview of semiconductor physics without indulging in extraneous solid state matters. The idea seems to have found a niche and the book has been repeatedly updated. In view of new developments in quantum entanglement and the interest in quantum computing, the latest edition includes new chapters on charge transport.

The Physics of Foams

by Denis Weare and Stefan Hutzler, Oxford University Press, ISBN 0 19 850551 5 (£47.50, 250 pages).

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This is a specialized but wonderful monograph that begins: “Pour a bottle of beer. Restraining your thirst for one moment, admire its lively performance (see figure 1.1).” This book is also a lively performance – its authors, from Dublin’s Trinity College, evidently have a knowledge for thirst!

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