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This book proposes a theory of analogical arguments, with special focus on analogies in mathematics and science. The core principle of the theory is that a good analogical argument must articulate a clear relationship capable of generalization. This idea leads to a set of distinct models for the critical analysis of prominent forms of analogical argument, corresponding to different logical, causal and probabilistic relationships that occur in scientific reasoning. The same principle allows us to relate analogical reasoning to broad norms and values of scientific practice, such as symmetry and unification. Elaborating this principle, the book raises questions and proposes answers regarding (1) criteria for evaluating analogical arguments, (2) the philosophical justification for analogical reasoning, and (3) the place of scientific analogies in the context of theoretical confirmation.

The investigation of discrete symmetries is a fascinating subject which has been central to the agenda of physics research for fifty years, and has been the target of many experiments, ongoing and in preparation, all over the world. This book approaches the subject from a somewhat less traditional angle: it puts more emphasis on the experimental aspects of the field, trying to provide a wider picture than usual and to convey the intellectual challenge of experimental physics. The book includes the related connection to phenomenology, a purpose for which the precision experiments in this field — often rather elegant and requiring a good amount of ingenuity — are very well suited. The book discusses discrete symmetries (parity, charge conjugation, time reversal, and of course CP symmetry) in microscopic (atomic, nuclear, and particle) physics, and includes a detailed description of some key or representative experiments. The book discusses their principles and challenges more than the historical development. The main past achievements and the most recent developments are both included.

The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.

This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.

This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.

This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into and modify this framework. The book then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, the book also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a useful book for students and practitioners in the natural and social sciences, with new material even for the experts.

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper understanding of quantum field theory and has played an increasingly important role in the theory over the past twenty years. This book presents all the different aspects of the study of anomalies in an accessible and self-contained way. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. This approach is followed here, and the derivations and calculations are given explicitly. Topics discussed include the relevant ideas from differential geometry and topology and the application of these paths (path integrals, differential forms, homotopy operators, etc.) to the study of anomalies. Chapters are devoted to abelian and nonabelian anomalies, consistent and covariant anomalies, and gravitational anomalies.

The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. students and postdoctoral Fellows with the principles and methods of modern lattice field theory, which Is set to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the courses of the school began by covering lattice theory basics (P. Hernández), lattice renormalization and improvement (P. Weisz and A. Vladikas) and the many faces of chirality (D.B. Kaplan). A later course introduced QCD at finite temperature and density (O. Philipsen). A broad view of lattice computation from the basics to recent developments was offered in the corresponding course (M. Lüscher). The students learned the basics of lattice computation in a hands-on tutorial (S. Schaefer)---a first at Les Houches, Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants has been covered in the course on chiral perturbation theory (M. Golterman). A course in heavy-quark effective theories (R. Sommer), an essential tool for performing the relevant lattice calculations, covered HQET from its basics to recent advances. A number of shorter courses rounded out the school and broadened its purview. These included recent applications to flavour physics (L. Lellouch) the nucleon--nucleon interation (S. Aoki) and a course on physics beyond the Standard Model (T. Appelquist and E.T. Neil).

This book is a thorough and up‐to‐date introduction to black hole physics. It provides a modern and unified overview of all their aspects, physical, mathematical, astrophysical, classical, and quantum. Black holes are the most intriguing objects in the Universe. For many years they have been considered just as interesting solutions of the General Relativity with a number of amusing mathematical properties. But now, after discovery of astrophysical black holes, the Einstein gravity has become a practical tool for their study. In this book we present the theory of black holes in the form which might be useful for students and young scientists. This is a self‐contained textbook. It includes pedagogically presented `standard' material on black holes and also quite new subjects such as black holes in spacetimes with large extra dimensions and a role of hidden symmetries in black hole physics.