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From the Web to the Grid and Beyond: Computing Paradigms Driven by High-Energy Physics

By René Brun, Federico Carminati and Giuliana Galli Carminati (eds.)
Springer
Hardback: £62.99 €74.85 $99.00
E-book: £49.99 €59.49 $69.95
Also available at the CERN bookshop

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To tell the story behind the title, the editors of this book have brought together chapters written by many well-known people in the field of computing in high-energy physics.

It starts with enlightening accounts by René Brun and Ben Segal of how things that I have been familiar with since being a postdoc came to be. I was intrigued to discover how we alighted on so much of what we now take for granted, such as C++, TCP/IP, Unix, code-management systems and ROOT. There is a nice – and at times frightening – account of the environment in which the World Wide Web was born, describing the conditions that needed to be present for it to happen as it did, and which nearly might not have been the case. The reader is reminded that ground-breaking developments in high-energy physics do not, in general, come about from hierarchical management plans, but from giving space to visionaries.

There are several chapters on the Grid (Les Robertson, Patricia Méndez Lorenzo and Jamie Shiers) and the evolution from grids to clouds (Pedrag Buncic and Federico Carminati). These will be of interest to those who, like me, were involved in a series of EU Grid projects that absorbed many of us completely during the era of “e-science”. The Worldwide LHC Computing Grid was built and is of course now taken for granted by all of us. The discussion of virtualization and the evolution from grids to clouds presents an interesting take on what is a change of name and what is a change of technology.

In another chapter, Carminati gives his candid take on software development – and I found myself smiling and agreeing. Many of us will remember when some sort of religion sprang up around OO design methods, UML, OMT, software reviews and so on. He gives his view of where this helped and where it hindered in our environment, where requirements change, users are developers, and forward motion is made by common consent not by top-down design.

Distributed data and its access is discussed in depth by Fabrizio Furano and Andrew Hanushevsky, who remind us that this is one of the most demanding sectors in computing for high-energy physics. A history of parallel computing by Fons Rademakers is interesting because this has become topical recently, as we struggle to deal with many-core devices. Lawrence Pinsky’s chapter on software legal issues delves into how instruments such as copyright and patents are applied in an area for which they were never designed. It makes for engrossing reading, in the same way that technical issues become captivating when watching legal drama on television.

It is not clear – to me at least – whether Giuliana Galli Carminati’s final chapter on “the planetary brain” is a speculation too far and should be politely passed over, as the author invites the reader to do, or whether there is something significant there that the reader should be concerned about. The speculation is whether the web and grid form something that could be considered as a brain on a planetary scale. I leave you to judge.

It is a highly interesting book, and I plan to read many of the chapters again.

 

The Future Circular Collider study

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More than 350 world experts in accelerators and particle physics, including several laboratory directors, came together at the University of Geneva on 12–15 February to launch the Future Circular Collider (FCC) study, which will examine options for an energy-frontier collider based on a new 80–100-km-circumference tunnel infrastructure. The FCC study, which will be organized as a worldwide international collaboration, comprises a 100 TeV proton (and heavy-ion) collider at the energy frontier, a high-luminosity e+e (H, Z, W, and tt) factory as a potential intermediate step, and an analysis of options for a hadron-lepton collider. The goal of the study is to deliver a conceptual design report (CDR) together with a cost review by 2018, in time for the next update of the European Strategy for Particle Physics. The CDR will integrate physics, detector, accelerator and infrastructure aspects.

The FCC design study responds to a high-priority request in the 2013 update of the European Strategy for Particle Physics (CERN Courier July/August 2013 p9) stating that “A conceptual design study of options for a future high-energy frontier circular collider at CERN for the post-LHC era shall be carried out”. February’s kick-off meeting was co-sponsored by the Extreme Beams work package 5 of the EuCARD-2 project, within the European Commission’s FP7 Capacities Programme. Participants came from all over the world, with particularly strong representation from China, Japan, Russia and the US, in addition to the many attendees from laboratories and universities across Europe. The goals of the meeting were to introduce the FCC study, to discuss its scope and organization, and to prepare and establish global collaborations.

In his opening address, CERN’s director-general, Rolf Heuer, presented an exciting perspective and explained the main motivations for the FCC, while also cautioning that it was too early to make any cost estimate. Nima Arkani-Hamed of the Institute for Advanced Study in Princeton, and recently appointed as the first director of the Centre for Future High Energy Physics at the Institute of High Energy Physics (IHEP) in Beijing, highlighted the compelling physics case for the 100 TeV hadron collider. Precision physics will be essential at both the lepton and hadron colliders, as Christoph Grojean from the Institut de Física d’Altes Energies in Barcelona underlined.

A similar study for a 50–70 km, double-purpose lepton and hadron collider is being pursued in China, with an attractive site proposal and ambitious schedule. In presenting the project, Yifang Wang, director of IHEP in Beijing, conceded that it would be a difficult project but it would also be very exciting. Even if implemented somewhere other than in China, it would still be beneficial to the field of particle physics in general and to the Chinese high-energy physics and scientific community in particular. To this end, IHEP fully supports a global effort. Fermilab’s associate director for accelerators, Stuart Henderson, also reported a broad acknowledgement in the US that any future collider would need to be a global enterprise, requiring financial and human resources from across the world. He stressed that the US community wishes to play a role in any future collider, while also mentioning several domestic “grass-roots” activities.

Frédérick Bordry, CERN’s director of accelerators and technology, presented the roadmap for CERN. Europe’s top priority for the next two decades is the exploitation of the LHC, with nominal parameters and a total integrated luminosity of about 300 fb–1 by 2023, and with the High-Luminosity LHC upgrade to reach 3000 fb–1 by 2035 (CERN Courier January/February 2014 p12 and p23). In parallel, as one of the next-highest-priority items, the FCC design study will be pursued along with CLIC as a potential post-LHC accelerator project at CERN. Michael Benedikt, the FCC study co-ordinator, reviewed the baseline parameters, design challenges and preparations for global collaboration, stressing that new partner institutes will be welcome throughout the duration of the study. Key technologies are high-field magnets for the hadron collider and an efficient high-power superconducting RF (SRF) system for the lepton collider. Possible R&D goals for the study include the development of short 16-T dipole models in all regions (America, Asia and Europe) by 2018 and, in parallel, demonstration of 20-T magnet technology based on the combination of high- and low-temperature superconductors as well as SRF developments, targeted at overall optimization of system efficiency and cost.

Philippe Lebrun, former head of CERN’s Accelerator Technology Department, pointed out that, although CERN’s experience in building machines of increasing size and performance can be applied to the study of 80–100 km circular accelerators in the Geneva basin, the step from the 27 km Large Electron–Positron collider and the LHC to the FCC represents major challenges. These will require inventive solutions in accelerator science and technology as well as in conventional facilities. Felix Amberg from Amberg Engineering – a company involved in the Gotthard Base Tunnel project – reported and analysed specific aspects of building long tunnels. His presentation suggested that tunnelling costs and risks can be predicted fairly reliably, provided that the project does not extend over too long a time interval and that the legal framework remains stable during the construction period.

Worldwide collaboration in all areas – physics, experiments and accelerators – was found to be essential to reach the level for a CDR by 2018

After two days of plenary sessions, which surveyed the scope, plan, international situation and design starting points of the FCC, seven parallel sessions gave space for feedback, additional presentations and lively international discussions. Worldwide collaboration in all areas – physics, experiments and accelerators – was found to be essential to reach the level for a CDR by 2018. Key R&D areas for the FCC, such as superconducting high-field magnets and SRF, are of general interest and relevant for many other applications. Significant R&D investments have been made over the past decade(s), for example in the framework of the LHC and High-Luminosity LHC. Further continuation will ensure efficient use of these investments. At the kick-off meeting a consensus emerged on the approach to form a global collaboration for this study, and many participants expressed a strong interest – both for themselves and their institutes.

Institutes worldwide are now invited to join the global FCC effort, and to submit non-committing written “expressions of interest” with regard to specific contributions by the end of May 2014.

The 1980s: spurring collaboration

The 1980s were characterized by two outstanding achievements that were to influence the long-term future of CERN. First came the discovery of the W and Z particles, the carriers of the weak force, produced in proton–antiproton collisions at the Super Proton Synchrotron (SPS) and detected by the UA1 and UA2 experiments. These were the first, now-typical collider experiments, covering the full solid angle and requiring large groups of collaborators from many countries. The production of a sufficient number of antiprotons and their handling in the SPS underlaid these successes, which were crowned by the Nobel Prize awarded to Carlo Rubbia and Simon van der Meer in 1984.

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Then came the construction and commissioning of the Large Electron–Positron (LEP) collider. With its 27 km tunnel, it is still the largest collider of this kind ever built. Four experiments were approved – ALEPH, DELPHI, L3 and OPAL – representing again a new step in international co-operation. More than 2000 physicists and engineers from 12 member states and 22 non-member states participated in the experiments. Moreover, most of the funding of several hundred million Swiss francs had to come from outside the organization. CERN contributed only about 10% and had practically no reserves in case of financial overruns. Therefore the collaborations had to achieve a certain independence, and had to learn to accept common responsibilities. A new “sociology” for international scientific co-operation was born, which later became a model for the LHC experiments.

A result of the worldwide attraction of LEP was that from 1987 onwards, more US physicists worked at CERN than particle physicists from CERN member states at US laboratories. In Europe, two more states joined CERN: Spain, which had left CERN in 1968, came back in 1983, and Portugal joined in 1985. However, negotiations at the time with Israel and Turkey failed, for different reasons.

But the 1980s also saw “anti-growth”. Previously, CERN had received special allocations to the budget for each new project, leading to a peak around 1974 and declining afterwards. When LEP was proposed in 1981, the budget was 629 million Swiss francs. After long and painful discussions, Council approved a constant yearly budget of 617 million Swiss francs for the construction of LEP, under the condition that any increase – including automatic compensation for inflation – across the construction period of eight years was excluded. The unavoidable consequence of these thorny conditions was the termination of many non-LEP programmes (e.g. the Intersecting Storage Rings and the bubble-chamber programme) and a “stripped down” LEP project. The circumference of the tunnel had to be reduced, but was maintained at 27 km in view of a possible proton–proton collider in the same tunnel – which indeed proved to be a valuable asset.

A precondition to building LEP with decreasing resources was the unification of CERN. CERN II had been established in 1971 for construction of the SPS, with its own director-general, staff and management. From 1981, CERN was united under one director-general, but staff tended to adhere to their old groups, showing solidarity with their previous superiors and colleagues. However, for the construction of LEP, all of CERN’s resources had to be mobilized, and about 1000 staff were transferred to new assignments.

Another element of “anti-growth” had long-term consequences. Council was convinced that the scientific programme was first class, but had doubts about the efficiency of management. An evaluation committee was established to assess the human and material resources, with a view to reducing the CERN budget. In the end, the committee declined to consider a lower material budget because this would undoubtedly jeopardize the excellent scientific record of CERN. They proposed instead a reduction of staff from about 3500 to 2500, through an early retirement programme, and during the construction of the LHC this was even lowered to 2000. However, to cope with the increasing tasks and the rising number of outside users, many activities had to be outsourced, so considerable reduction of the budget was not achieved.

Yet despite these limiting conditions, LEP was built within the foreseen time and budget, thanks to the motivation and ingenuity of the CERN staff. First collisions were observed on 13 August 1989.

The theme of CERN’s 60th anniversary is “science for peace” – from its foundation, CERN had the task not only to promote science but also peace. This was emphasized at a ceremony for the 30th anniversary in 1984, by the American physicist and co-founder of CERN, Isidor Rabi: “I hope that the scientists of CERN will remember…[they are] as guardians of this flame of European unity so that Europe can help preserve the peace of the world.” Indeed during the 1980s, CERN continued to fulfil this obligation, with many examples such as co-operation with East European countries (in particular via JINR, Dubna) and with countries from the Far East (physicists from Mainland China and Taiwan were allowed to work together in the same experiment, L3, on LEP). Later, CERN became the cradle of SESAME, an international laboratory in the Middle East.

Unavoidably, CERN’s growth into a world laboratory is changing how it functions at all levels. However, we can be confident that it will perform its tasks in the future with the same enthusiasm, dedication and efficiency as in the past.

The Theory of the Quantum World: Proceedings of the 25th Solvay Conference on Physics

By David Gross, Marc Henneaux and Alexander Sevrin (eds.)
World Scientific
Hardback: £58
Paperback: £32
E-book: £24

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Since 1911, the Solvay Conferences have helped shape modern physics. The 25th edition in October 2011, chaired by David Gross, continued this tradition, while also celebrating the conferences’ first centennial. The development and applications of quantum mechanics have been the main threads throughout the series, and the 25th Solvay Conference gathered leading figures working on a variety of problems in which quantum-mechanical effects play a central role.

In his opening address, Gross emphasized the success of quantum mechanics: “It works, it makes sense, and it is hard to modify.” In the century since the first Solvay Conference, the worry expressed by H A Lorentz in his opening address in 1911 – “we have reached an impasse; the old theories have been shown to be powerless to pierce the darkness surrounding us on all sides” – has been resolved. Physics is not in crisis today, but as Gross says there is “confusion at the frontiers of knowledge”. The 25th conference therefore addressed some of the most pressing open questions in the field of physics. As Gross admits, the participants were “unlikely to come to a resolution during this meeting….[but] in any case it should be lots of fun”.

The proceedings contain the rapporteur talks and, in the Solvay tradition, they also include the prepared comments to these talks. The discussions among the participants – some involving dramatically divergent points of view – have been carefully edited and are reproduced in full.

The reports cover the seven sessions: “History and reflections” (John L Heilbron and Murray Gell-Mann); “Foundations of quantum mechanics and quantum computation” (Anthony Leggett and John Preskill); “Control of quantum systems” (Ignacio Cirac and Steven Girvin); “Quantum condensed matter” (Subir Sachdev); “Particles and fields” (Frank Wilczek); and “Quantum gravity and string theory” (Juan Maldacena and Alan Guth). The proceedings end – as did the conference – with a general discussion attempting to arrive at a synthesis, where the reader can judge if it fulfilled the prediction by Gross and was indeed “lots of fun”.

Mathematics of Quantization and Quantum Fields

By Jan Dereziński and Christian Gérard
Cambridge University Press
Hardback: £90 $140
Also available as an e-book

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Unifying a range of topics currently scattered throughout the literature, this book offers a unique review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, such as tensors, algebras, Fock spaces, and CCR and CAR representations. Applications of these topics to physical problems are discussed in later chapters.

Three-Particle Physics and Dispersion Relation Theory

By A V Anisovich, V V Anisovich, M A Matveev, V A Nikonov, J Nyiri and A V Sarantsev
World Scientific
Hardback: £65
E-book: £49

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The necessity of describing three-nucleon and three-quark systems has led to continuing interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes that are connected to the reaction in question by the unitarity condition or by virtual transitions. In the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.

Science, Religion, and the Search for Extraterrestrial Intelligence

By David Wilkinson
Oxford University Press
Hardback: £25
Also available as an e-book

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With doctorates in both astrophysics and theology, David Wilkinson is well qualified to discuss the subject matter of this book. He provides a captivating narrative on the scientific basis for the search for extraterrestrial intelligence and the religious implications of finding it. However, the academic nature of the writing might hinder the casual reader, with nearly every paragraph citing at least one reference.

Scientific and religious speculation on the possibility of life elsewhere in the universe is age-old. Wilkinson charts its history from the era of Plato and Democritus, where the existence of worlds besides our own was up for debate, to the latest data from telescopes and observatories, which paint vivid pictures of the many new worlds discovered around alien suns.

Readers familiar with astrophysics and evolutionary biology might find themselves skipping sections of the book that go into the specific conditions that need to be met for Earth-like life to evolve and attain intelligence. Wilkinson, however, is able to tie these varied threads together, presenting both the pessimism and optimism towards the presence of extraterrestrial life exhibited by scientists from different fields.

Despite referring to religion in the title, Wilkinson states early on that his work mainly discusses the relationship of Christianity and SETI. In this regard, the book provided me with much insight into Christian doctrine and its many – often contradictory – views on the universe. For example, despite the shaking of the geocentric perspective with the so-called Copernican Revolution, some Christian scholars from the era maintained that the special relationship of humans with God dictated that only Earth could harbour God-fearing life forms. Earth, therefore, retained its central position in the universe in a symbolic if not a literal sense. Other views held that nothing could be beyond the ability of an omnipotent, omnipresent God, who to showcase his glory might well have created other worlds with their own unique creatures.

After covering everything from science fiction to Christian creation beliefs, Wilkinson concludes with his personal views on the value of involving theology in searches for alien life. I leave you to draw your own conclusions about this! Overall, the book is a fascinating read and is recommended for those pondering the place of humanity in our vast universe.

Einstein’s Physics: Atoms, Quanta, and Relativity – Derived, Explained, and Appraised

By Ta-Pei Cheng
Oxford University Press
Hardback: £29.99
Also available as an e-book

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Being familiar with the work of Ta-Pei Cheng, I started this book with considerable expectations – and I enjoyed the first two sections. I found many delightful discussions of topics in the physics that came after Albert Einstein, as well as an instructive discussion on his contributions to quantum theory, where the author shares Einstein’s reservations about quantum mechanics. However, the remainder of the text dedicated to relativity and related disciplines has problems. The two pivotal issues of special relativity, the aether and the proper time, provide examples of what I mean.

On p140, the author writes “…keep firmly in mind that Einstein was writing for a community of physicists who were deeply inculcated in the aether theoretical framework”, and continues “(Einstein, 1905) was precisely advocating that the whole concept of aether should be abolished”. Of course, Einstein was himself a member of the community “inculcated in the aether” and, indeed, aether was central in his contemplation of the form and meaning of physical laws. His position was cemented by the publication in 1920 of a public address on “Aether and the Theory of Relativity” and its final paragraph “…there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time…”. This view superseded the one expressed in 1905, yet that is where the discussion in the book ends.

The last paragraph on p141 states that “…the key idea of special relativity is the new conception of time.” Einstein is generally credited with the pivotal discovery of “body time”, or in Hermann Minkowski’s terminology, a body’s “proper time”. The central element of special relativity is the understanding of the invariant proper time. Bits and pieces of “time” appear in sections 9–12 of the book, but the term “proper time” is mentioned only incidentally. Then on p152 I read “A moving clock appears to run slow.” This is repeated on p191, with the addition “appears to this observer”. However, the word “appears” cannot be part of an unambiguous explanation. A student of Einstein’s physics would say “A clock attached to a material body will measure a proper-time lifespan independent of the state of inertial motion of the body. This proper time is the same as laboratory time only for bodies that remain always at rest in the laboratory.” That said, I must add that I have never heard of doubts about the reality of time dilation, which is verified when unstable particles are observed.

Once the book progresses into a discussion of Riemannian geometry and, ultimately, of general relativity, gauge theories and higher-dimensional Kaluza–Klein unification, it works through modern topics of only marginal connection to Einstein’s physics. However, I am stunned by several comments about Einstein. On p223, the author explains how “inept” Einstein’s long proof of general relativity was, and instead of praise for Einstein’s persistence, which ultimately led him to the right formulation of general relativity, we read about “erroneous detours”. On p293, the section on “Einstein and mathematics” concludes with a paragraph that explains the author’s view as to why “…Einstein had not made more advances…”. Finally, near the end, the author writes on p327 that Einstein “could possibly have made more progress had he been as great a mathematician as he was a great physicist”. This is a stinging criticism of someone who did so much, for things he did not do.

The book presents historical context and dates, but the dates of Einstein’s birth and death are found only in the index entry “Einstein”, and there is little more about him to be found in the text. A listing of 30 cited papers appears in appendix B1 and includes only three papers published after 1918. The book addresses mainly the academic work of Einstein’s first 15 years, 1902–1917, but I have read masterful papers that he wrote during the following 35 years, such as “Solution of the field of a star in an expanding universe” (Einstein and Straus 1945 Rev. Mod. Phys. 17 120 and 1946 Rev. Mod. Phys. 18 148).

I would strongly discourage the target group – undergraduate students and their lecturers – from using this book, because in the part on special relativity the harm far exceeds the good. To experts, I recommend Einstein’s original papers.

Greater than the sum of the parts

Agnieszka Zalewska

CERN was founded in 1954 with the aim of bringing European countries together to collaborate in scientific research after the horrors of the Second World War. After the end of the war, however, Europe had been divided politically by the “Iron Curtain”, and countries in the Eastern Bloc were not in a position to join CERN. Nevertheless, through personal contacts dating back to pre-war days, scientists on either side of the divide were able to keep in touch. From the start, CERN had schemes to welcome physicists from outside its member states. At the same time, the bubble-chamber experiments in particular provided a way that research groups in the East could contribute to physics at CERN from their home institutes. The groups could analyse bubble-chamber events with relatively few resources and make their mark by choosing specific areas of analysis.

In the case of my country, Poland, this contact with CERN from the 1950s provided a precious window on modern science, allowing us to maintain a good level in particle physics. The first Polish physicist was welcomed to the laboratory in 1959 and was soon followed by others when CERN awarded several scholarships to young researchers from Cracow and Warsaw. Collaboration between CERN and Polish institutes followed, and despite the difficult circumstances, physicists in Poland were able to make important contributions to CERN’s research programmes. In 1963, the country gained observer status at CERN Council, as the only country from Eastern Europe.

My association with CERN began when I was a student at the Jagellonian University in Cracow in the early 1970s, working on the analysis of events collected by the 2-m bubble chamber. During the 1960s, the experimental groups in Cracow and Warsaw had made the analysis of high-multiplicity events their speciality, and this was the topic for my doctoral thesis. The collaborative work with CERN gradually extended to electronic detectors, and from the 1970s Polish groups contributed hardware such as wire chambers to a number of experiments. The DELPHI experiment at the Large Electron–Positron (LEP) collider already used a variety of Polish contributions to both hardware and software.

It is hard today to imagine the world without the web. It was CERN’s gift to humanity

The start-up of LEP coincided with the big political changes in Eastern Europe at the end of the 1980s. Poland became the first former Eastern Bloc country to be invited to become a CERN member state, and in July 1991 my country became the 16th member of CERN – a moment of great pride. Hungary, the Czech Republic and Slovakia followed soon after.

The end of the 1980s also coincided with the development of the World Wide Web to help the large collaborations at LEP work together. It revolutionized the way we could work in our home institutions. In particular in Poland, a dedicated phone line set up in 1991 between CERN and the institutes in Cracow and Warsaw provided a “magic” link, allowing us, for example, to make changes remotely to software running underground at LEP.

It is hard today to imagine the world without the web. It was CERN’s gift to humanity – creating connections, allowing the exchange of ideas and communication between people all over the world. Developed in a scientific, non-commercial organization, the web’s international annual economic value is now estimated at €1.5 trillion. As Chris Llewellyn Smith, CERN’s director-general from 1994 to 1998, asked: how many yearly budgets of CERN have been saved because it was developed quickly in a non-commercial environment?

Now, after some four decades in particle physics, I have the enormous privilege to be president of CERN Council. I have already experienced the exceptional moment when the Israeli flag was raised for the first time at the Meyrin entrance to the laboratory, representing the first new member state to join the organization for 14 years. Other countries are at various stages in the process of accession to become member states or to attain associate membership. In discussions with the physicists from these countries, I recognize the same feelings that we had in countries like Poland in the 1960s or 1970s.

As one person said to me recently, it is not only CERN as the organization, but the idea of CERN that has such a strong appeal. It brings people together from different nationalities and cultures, people who have different ways of doing things – and this brings added value. CERN really is something where the whole is greater than the sum of the parts, as we all work together towards a common goal – a noble goal – to learn more about the universe that we inhabit.

During the past 60 years, the idea of CERN has succeeded in the goal of bringing European countries to work peacefully together, helping to bridge the divisions that existed between East and West. I sincerely believe that this “idea” will continue to inspire people around the world for years to come.

Quantum Field Theories in Two Dimensions: Collected Works of Alexei Zamolodchikov (2 volumes)/

By Alexander Belavin, Yaroslav Pugai and Alexander Zamolodchikov (ed.)
World Scientific
Hardback: £124

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These two volumes contain original contributions of Alexei Zamolodchikov (1952–2007), who was a prominent theoretical physicist of his time. Volume 1 contains his work on conformal field theories, 2D quantum gravity and Liouville theory. Volume 2 includes his pioneering work on non-perturbative methods in 2D quantum field theory and on integrable models. Both volumes can be used as an advanced textbook by graduate students specializing in string theory, conformal field theory and integrable models of quantum field theory. They are also highly relevant to experts in these fields.

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