**The Quantum Theory of Fields III: Supersymmetry** by

Steven Weinberg, Cambridge University Press, ISBN 0 521

66000 9 (hbk £32.50/$49.95).

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 (10^{19}GeV). 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

Summer School of Gif-sur-Yvette

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 for

supersymmetry 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.*Sergio Ferrara,
CERN.*

**Lucifer’s Legacy: the Meaning of
Asymmetry**by Frank Close, Oxford University Press,

ISBN 0 19 850380 6.

Communicating science is difficult.

In contrast with other fields, it needs long experience before

being able to contribute. While creativity in science or the arts is

often left to younger people with open minds, when it comes to

explaining new developments to a wide audience, the science

communicator first has to master the science itself, its teaching

and its popular dissemination.

Frank Close, who has

already provided several popular science standards, has all it

requires. Here he takes us on a tour of modern science,

following a theme, the study of which started early in 19th

century: the fascination and appeal of the underlying symmetry

of nature, and its attendant asymmetry.

The tour begins

and ends in Paris, in a French garden where almost perfect

symmetry appears slightly broken, that day, by a damaged

statue of Lucifer. With this metaphor of our entire world,

accidentally asymmetric but governed by apparently symmetric

laws, Close embarks on a journey through the history of the

quest to understand where the asymmetry of the universe

comes from.

This governs even our own existence:

matter overcoming antimatter was a necessary step for there to

be anything at all. Moreover, life on Earth, seen through the

basic structure of organic molecules, is asymmetric. The

mystery of life cannot be understood by physics alone, yet

asymmetry is a property of life itself, and this thread continues

throughout the book.

First the author reviews symmetry

at large, with examples taken from everyday life, featuring

common notions and clichés. One of the enigmas dealt with is

my own favourite, Martin Gardner’s puzzle: why does a mirror

invert left and right, but not top and bottom? Here the author

adds much of his own insight and wit (“the muscles which close

a mouth are stronger than those which open it – as is well

known to all who have sat in committees”). The result is a

fascinating panorama, down to the molecular level, of the

asymmetries around us, which have first to be discovered

before being explained.

The remainder of the book

covers the history of the tools needed to explore matter and to

reveal its hidden asymmetries. Following the pioneer work of

Biot (polarization of light) and Pasteur (study of racemic acid),

the end of the 19th century brought major discoveries by

scientists investigating the true nature of electricity, continuing

the route taken by Faraday and Maxwell.

First came the

discovery of X-rays by Roentgen, a key tool for decoding DNA

structure half a century later. Immediately after X-rays came

the discovery of the electron by Thomson, and then of

radioactivity (Becquerel and the Curies) and the nucleus

(Rutherford). The major cornerstones of modern physics were

revealed during those few “magic” years, and they are narrated

by Close in a way that reveals the hesitations and inspirations of

the actors, the banal errors of those who “could have found”

(Lenard, Crookes) but were not quite ready, and the genius of

those who made sure that they were in the right place at the

right time with the right ideas. What better plea could there be

for fundamental research?

All of this leads to modern

physics, exploiting the concept of symmetry in a profound way,

revealing hitherto unsuspected laws through delicate symmetry

breaking. We are introduced to unification schemes based on

symmetries broken at our energy scale, but revealed in

high-energy experiments. Close explains this in detail and with

amusing anecdotes, and how it guided physicists during their

major discoveries of the secrets of the matter, right up to the

next foreseen step – the quest to find the Higgs

boson.

The instrumentation and apparatus required for

this quest are impressive. The incredible effort of a worldwide

community at CERN for the LHC and its giant experiments

help the reader to become familiar with this ultimate search for

the origin of mass.

On the way, the chapter on antimatter

deserves admiration: antimatter is one of the most difficult

notions scientists have to explain. I remember a colleague

beginning a public talk by unapologetically defining antimatter

as “the negative energy solution to Dirac’s equations”. What is

exact is not always clear, and Frank Close takes the time to

introduce antimatter, to draw its human side through Dirac’s

character and by noting the time it took, from Dirac’s work in

1928 to Anderson’s discovery of the positron in

1932.

The violation of “mirror” P symmetry by the weak

force, how this was discovered, the violation of CP symmetry

and recent evidence for the violation of time symmetry are all

clearly explained, illustrated by analogies with Escher prints to

help the mind see patterns in abstract spaces.

We then

understand that the universe, once fully symmetric, exhibited

asymmetries when freezing, which enabled life to be. Life,

intrinsically related to asymmetries, is the theme of this book,

and Close revisits what has already been written on this theme,

offering us an absorbing and scientifically correct account of

symmetry and its deep implications.*Yves Sacquin,
Saclay.*

**Cosmology: the Science of the
Universe**by Edward Harrison, Cambridge University Press,

ISBN 0 521 66148 X (£32.50/$54.95).

A great deal has

happened to our understanding of the universe in the almost 20

years since the first edition of “Cosmology” became a bestseller.

Now Prof. Harrison has produced this updated and extended

second edition. It has many new sections and revisions and it is

wonderfully informative and authoritative on an amazingly

wide range of topics.

My own particular favourites are

his treatment of Special Relativity – just the way particle

physicists like it – and his explanation of Olbers’ paradox – the

clearest I’ve ever seen. The entire book is quirky and

entertaining, peppered with historical facts, extremely

perceptive questions, and provocative and challenging issues for

discussion. All of this comes with essentially no mathematics in

a very satisfactory and readable introductory overview of

modern cosmology.*Steve Reucroft, Northeastern
University.*