Bookshelf

• Lectures on Quantum Mechanics • Stochastic Cooling of Particle Beams • Basic Concepts of String Theory

Lectures on Quantum Mechanics
By Steven Weinberg
Cambridge University Press
Hardback: £40 $75

This is a beautifully written book that is crafted with precision and is full of insight. However, this is for most people not the book from which to learn quantum mechanics for the first time. The cover notes acknowledge this and the book is advertised as being “ideally suited to a one-year graduate course” and “a useful reference for researchers”. That is not to say that it deals only with advanced material – the theory is built up from scratch and the logical structure is quite traditional.

The book starts with a careful exposition of the early history and the Schrödinger-equation analysis of the hydrogen atom and the harmonic oscillator, before moving on to cover the general principles, angular momentum and symmetries. The middle part of the book is concerned with approximate methods and develops the theory starting from time-independent perturbations and ending with the general theory of scattering. The final part deals mainly with the canonical formalism and the behaviour of a charged particle in an electromagnetic field, including the quantization of the field and the emergence of photons. The final chapter covers entanglement, the Bell inequalities and quantum computing, all in a mere 14 pages.

Perhaps what distinguishes this book from the competition is its logical coherence and depth, and the care with which it has been crafted. Hardly a word is misplaced and Weinberg’s deep understanding of the subject matter means that he leaves no stone unturned: we are asked to accept very little on faith. Examples include Pauli’s purely algebraic calculation of the hydrogen spectrum, the role of the Wigner-Eckhart theorem in a proper appreciation of the Zeeman effect and in atomic selection rules, as well as the emergence of geometrical phases. There is also a thoughtful section on the interpretations of quantum mechanics.

Weinberg has a characteristic style – his writing is full of respect for the reader and avoids sensational comments or attempts to over-emphasize key points. The price we pay is that the narrative is rather flat but in exchange we gain a great deal in elegance and content – it is for the reader to follow Weinberg in discovering the joys of quantum mechanics through a deeper level of understanding: I loved it!

Jeff Forshaw, University of Manchester.

Stochastic Cooling of Particle Beams
By Dieter Möhl
Springer
Paperback: £31.99 €36.87 $39.50
E-book: £24.99 €29.74 $49.95

Over the past decades, stochastic cooling of particle beams has grown, thrived and led to breathtaking results in physics from accelerator labs around the world. Now, great challenges lie ahead in the context of future projects, which strive for highly brilliant secondary-particle beams. For newcomers and researchers alike, there is no better place to learn about stochastic cooling than this book.

Dieter Möhl was one of the foremost experts in the field; ever since the beginning of the adventure in the 1970s, in the team of Simon van der Meer at CERN. Here he has surpassed himself to produce a personal book based not only on his masterful lectures over the years, but also covering, in the proper context and depth, additional subjects that have previously been dispersed across the specialized literature. He goes further by illustrating concepts with his recent personal studies on future projects (e.g. the accumulator ring RESR for the FAIR project) and is well placed to suggest innovations (e.g. alternative methods for stacking and momentum cooling, “split-function” lattices). Insightful remarks based on his experience, invaluable calculation recipes, realistic numerical examples, as well as an excellent bibliography go together to round up the whole book.

In this self-contained book, Möhl provides a superb pedagogical and concise treatment of the subject, from fundamental concepts up to advanced subjects. He describes the analytical formalism of stochastic cooling, stressing, whenever important, its interplay with the machine hardware and beam diagnostics.

The first six chapters introduce the ingredients of the state of the art of stochastic cooling. With deep insight, Möhl explains in chapter 2 all of the different techniques for betatron and/or momentum cooling. This is the most thorough yet compact overview that I know of, a great service to system designers and operators. In both the time-domain and frequency-domain pictures, the reader is guided step by step and with great clarity into delicate aspects of the subject (for instance, the mixing and power requirements) as well as rather complex calculations (such as for betatron cooling, the feedback via the beam and the cooling by nonlinear pickups and kickers). A great help to newcomers and a handy reference for the experts comes in the form of the comprehensive summary on the pickup and kicker impedances in chapter 3 as well as the discussion of the Schottky noise in chapter 4.

Chapter 7 deals with the Fokker-Planck equation and remarkably summarizes its most important application, namely in modelling the beam accumulation by stochastic cooling. The notoriously difficult bunched-beam cooling, which is of great interest for future colliders, is lucidly reviewed in chapter 8.

Dieter Möhl had practically finished the book when he unexpectedly passed away (CERN Courier January/February 2013 p44). Throughout this work of reference, his modesty and generosity emerge together with the quintessence of stochastic cooling, as part of his legacy.

Christina Dimopoulou, GSI/Darmstadt.

Basic Concepts of String Theory
By Ralph Blumenhagen, Dieter Lüst and Stefan Theisen
Springer
Hardback: £72 €84.35 $99
E-book: £56.99 €67.82 $69.95

This new textbook features an introduction to string theory, a fundamental line of research in theoretical physics during recent decades. String theory provides a framework for unifying particle physics and gravity in a coherent manner and, moreover, appears also to be consistent at the quantum level. This sets it apart from other attempts at that goal. More generally, string theory plays an important role as a generator of ideas and “toy” models in many areas of theoretical physics and mathematics; the spin-off includes the application of mathematical methods, originally motivated by and developed within string theory, to other areas. For example, string theory helps in the understanding of certain properties of gauge theories, black holes, the early universe and heavy-ion physics.

Thus any student and researcher of particle physics should have some knowledge of this important field. The book under discussion provides an excellent basis for that. It encompasses a range of essential and advanced topics, aiming at mid – to high-level students and researchers who really want to get into the subject and/or would like to look up some facts. For beginners, who just want to gain an impression of what string theory is all about, the book might be a little hefty and deterring. It really requires a serious effort to master it, and corresponds to at least a one-year course on string theory.

The book offers a refreshing mix of basic facts and up-to-date research, and avoids giving too much space to formal and relatively boring subjects such as the quantization of the bosonic string. Rather, the main focus is on the construction and properties of the various string theories in 10 dimensions and their compactifications to lower dimensions; it also includes thorough discussions of D-branes, fluxes and dualities. A particular emphasis is given to the two-dimensional world-sheet, or conformal field-theoretical point of view, which is more “stringy” than the popular supergravity approach. Filling this important gap is one of the strengths of this book, which sets it apart from other recent, similar books.

This is in line with the general focus of the book, namely the unification aspect of string theory, whose main aim is to explain, or at least describe, all known particles and interactions in one consistent framework. In recent years, additional aspects of string theory have been become increasingly popular and important lines of research, including the anti-de-Sitter/conformal-field-theory (AdS/CFT) correspondence and the quantum properties of black holes. The book barely touches on these subjects, which is wise because even the basic material would be more than would fit into the same book. For these subjects, a second volume may be in order.

All in all, this book is a perfect guide for someone with some moderate prior exposure to field and string theory, who likes to get into the principles and technical details of string model construction.

Wolfgang Lerche, CERN.