**From Photon to Neuron: Light, Imaging, Vision**

*By Philip Nelson*

**Princeton University Press 2017**

This book is as elegant as it is deep. A masterful tour of the science of light and vision. It goes beyond artificial boundaries between disciplines and presents all aspects of light as it appears in physics, chemistry, biology and the neural sciences.

The text is addressed to undergraduate students, an added challenge to the author, which is met brilliantly. Since many of the biological phenomena involved in our perception of light (in photosynthesis, image formation and image interpretation) happen ultimately at the molecular level, one is introduced rather early to the quantum treatment of the particles that form light: photons. And when they are complemented with the particle-wave duality characteristic of quantum mechanics, it is much easier to understand a large palette of natural phenomena without relying on the classical theory of light, embodied by Maxwell’s equations, whose mathematical structure is far more advanced than what is required. This classical approach has the problem that eventually one needs the quantisation of the electromagnetic field to bring photons into the picture. This would make the text rather unwieldly, and not accessible to a majority of undergraduates or biologists working in the field.

In the same way that the author instructs non-physics students in some basic physics concepts and tools, he also provides physicists with accessible and very clear presentations of many biological phenomena involving light. This is a textbook, not an encyclopaedia, hence a selection of such phenomena is necessary to illustrate the concepts and methods needed to develop the material. There are sections at the end of most chapters containing more advanced topics, and also suggestions for further reading to gain additional insight, or to follow some of the threads left open in the main text of the chapter.

A cursory perusal of the table of contents at the beginning will give the reader an idea of the breadth and depth of material covered. There is a very accessible presentation of the theory of colour, from a physical and biological point of view, and its psychophysical effects. The evolution of the eye and of vision at different stages of animal complexity, imaging, the mechanism of visual transduction and many more topics are elegantly covered in this remarkable book.

The final chapters contain some advanced topics in physics, namely, the treatment of light in the theory of quantum electrodynamics. This is our bread and butter in particle physics, but the presentation is more demanding on the reader than any of the previous chapters.

Unlike chapter zero, which explains the rudiments of probability theory in the standard frequentist and Bayesian approaches that can be understood basically by anyone familiar with high-school mathematics, chapters 12 and 13 require a more substantial background in advanced physics and mathematics.

The gestalt approach advocated by this book provides one of the most insightful, cross-disciplinary texts I have read in many years. It is mesmerising and highly recommendable, and will become a landmark in rigorous, but highly accessible interdisciplinary literature.

*Luis Álvarez-Gaumé, Stony Brook University, US.*

**Quantum Field Theory Approach to Condensed Matter Physics**

*By Eduardo C Marino*

**Cambridge University Press**

This book provides an excellent overview of the state of the art of quantum field theory (QFT) applications to condensed-matter physics (CMP). Nevertheless, it is probably not the best choice for a first approach to this wonderful discipline.

QFT is used to describe particles in the relativistic (high-energy intensity) regime, but, as is well known, its methods can also be applied to problems involving many interacting particles – typically electrons. The conventional way of studying solid-state physics and, in particular, silicon devices does not make use of QFT methods due to the success of models in which independent electrons move in a crystalline substrate. Currently, though, we deal with various condensed-matter systems that are impervious to that simple model and could instead profit from QFT tools. Among them: superconductivity beyond the Bardeen–Cooper–Schrieffer approach (high-temperature superconducting cuprates and iron-based superconductors), the quantum Hall effect, conducting polymers, graphene

and silicene.

The author, as he himself states, aims to offer a unified picture of condensed-matter theory and QFT. Thus, he highlights the interplay between these two theories in many examples to show how similar mechanisms operate in different systems, despite being separated by several orders of magnitude in energy. He discusses, for example, the comparison between the Landau–Ginzburg field of a superconductor with the Anderson–Higgs field in the Standard Model. He also explains the not-so-well-known relation between the Yukawa mechanism for mass generation of leptons and quarks, and the Peierls mechanism of gap generation in polyacetylene: the same trilinear interaction between a Dirac field, its conjugate and a scalar field that explains why polyacetylene is an insulator, is responsible for the mass of elementary particles.

The book is structured into three parts. The first covers conventional CMP (at advanced undergraduate level). The second provides a brief review of QFT, with emphasis on the mathematical analysis and methods appropriate for non-trivial many-body systems (as, in particular, in chapters eight and nine, where a classical and a quantum description of topological excitations are given). I found the pages devoted to renormalisation remarkable, in which the author clearly exposes that the renormalisation procedure is a necessity due to the presence of interactions in any QFT, not to that of divergences in a perturbative approach. The heart of the book is part three, composed of 18 chapters where the author discusses the state of the art of condensed-matter systems, such as topological insulators and even quantum computation.

The last chapter is a clear example of the non-conventional approach proposed by the author: going straight to the point, he does not explain the basics of quantum computation, but rather discusses how to preserve the coherence of the quantum states storing information, in order to maintain the unitary evolution of quantum data-processing algorithms. In his words, “the main method of coherence protection involves excitation, having the so-called non-abelian statistics”, which, going back to CMP, takes us to the realm of anyons and Majorana qubits. In my opinion, this book is not suitable for undergraduate or first-year graduate students (for whom I see as more appropriate, the classic *Condensed Matter Field Theory* by Altland and Simons). Instead, I would keenly recommend this to advanced graduate students and researchers in the field, who will find, in part three, plenty of hot topics that are very well explained and accompanied by complete references.

*Rogelio Palomo, University of Sevilla, Spain.*

**Books received**

**Applied Computational Physics**

*By Joseph Boudreau and Eric Swanson*

**Oxford University Press**

This book aims to provide physical sciences students with the computational skills that they will need in their careers and expose them to applications of programming to problems relevant to their field of study. The authors, who are professors of physics at the University of Pittsburgh, decided to write this text to fill a gap in the current scientific literature that they noticed while teaching and training young researchers. Often, graduate students have only basic knowledge of coding, so they have to learn on the fly when asked to solve “real world” problems, like those involved in physics research. Since this way of learning is not optimal and sometimes slow, the authors propose this guide for a more structured study.

Over almost 900 pages, this book introduces readers to modern computational environments, starting from the foundation of object-oriented computing. Parallel computation concepts, protocols and methods are also discussed early in the text, as they are considered essential tools.

The book covers various important topics, including Monte Carlo methods, simulations, graphics for physicists and data modelling, and gives large space to algorithmic techniques. Many chapters are also dedicated to specific physics applications, such as Hamiltonian systems, chaotic systems, percolation, critical phenomena, few-body and multi-body quantum systems, quantum field theory, etc. Nearly 400 exercises of varying difficulty complete the text.

Even though most of the examples come from experimental and theoretical physics, this book could also be very useful for students in chemistry, biology, atmospheric science and engineering. Since the numerical methods and applications are sometimes technical, it is particularly appropriate for graduate students.

**Classical Field Theory**

*By Joel Franklin*

**Cambridge University Press**

This book provides a comprehensive introduction to classic field theory, which concerns the generation and interaction of fields and is the logical precursor of quantum field theory. But, while in most university physics programmes students are taught classical mechanics first and then quantum mechanics, quantum field theory is normally not preceded by dedicated classic field theory classes. The author, though, claims that it would be worth giving more room to classical field theory, since it can offer a good way to think about modern physical model building.

The focus is on the relativistic structural elements of field theories, which enable a deeper understanding of Maxwell’s equations and of the electromagnetic field theory. The same also stands for other areas of physics, such as gravity.

The book comprises four chapters and is completed by three appendices. The first chapter provides a review of special relativity, with some in-depth discussion of transformations and invariants. Chapter two focuses on Green’s functions and their role as integral building blocks, offering as examples static problems in electricity and the full wave equation of electromagnetism. In chapter three, Lagrangian mechanics is introduced, together with the notions of a field Lagrangian and of action. The last chapter is dedicated to gravity, another classic field theory. The appendices include mathematical and numerical methods useful for field theories and a short essay on how one can take a compact action and from it develop all the physics known from EM.

Written for advanced-undergraduate and graduate students, this book is meant for dedicated courses on classical field theory, but could also be used in combination with other texts for advanced classes on EM or a course on quantum field theory. It could also be used as a reference text for self-study.