In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.

This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Natural computing brings together nature and computing to develop new computational tools for problem solving; to synthesize natural patterns and behaviors in computers; and to potentially design novel types of computers. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications presents a wide-ranging survey of novel techniqu

Nuclear magnetic resonance spectroscopy, which has evolved only within the last 20 years, has become one of the very important tools in chemistry and physics. The literature on its theory and application has grown immensely and a comprehensive and adequate treatment of all branches by one author, or even by several, becomes increasingly difficult. This series is planned to present articles written by experts working in various fields of nuclear magnetic resonance spectroscopy, and will contain review articles as well as progress reports and original work. Its main aim, however, is to fill a gap, existing in literature, by publishing articles written by specialists, which take the reader from the introductory stage to the latest development in the field. The editors are grateful to the authors for the time and effort spent in writing the articles, and for their invaluable cooperation. The Editors Analysis of NMR Spectra A Guide for Chemists R. A. HOFFMAN t S. FORSEN Division of Physical Chemistry, Chemical Center, Lund Institute of Technology, Lund, Sweden B. GESTBLOM Institute of Physics, University of Uppsala, Sweden Contents I. Principles of NMR Spectroscopy 4 1. 1. The Magnetic Resonance Phenomenon 4 a) Nuclear Moments. . . . . . . . 4 b) Magnetic Spin States and Energy Levels 5 c) The Magnetic Resonance Condition. 7 d) The Larmor Precession. . 7 e) Experimental Aspects . . . . 8 1. 2. Chemical Shifts . . . . . . . . 9 a) The Screening Constant 11. . . 9 b) Chemical Shift Scales (11 and r) 10 1. 3. Spin Coupling Constants 12 1. 4. Intensities. . . . . . . .

Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive investigations on frustrated spin systems have really started with the concept of frustration introduced at the same time by G Toulouse and by J Villain in 1977 in the context of spin glasses. The frustration is generated by the competition of different kinds of interaction and/or by the lattice geometry. As a result, in the ground state all bonds are not fully satisfied. In frustrated Ising spin systems, a number of spins behave as free spins. In frustrated vector spin systems, the ground-state configuration is usually non-collinear. The ground state of frustrated spin systems is therefore highly degenerate and new induced symmetries give rise to unexpected behaviors at finite temperatures. Many properties of frustrated systems are still not well understood at present. Theoretically, recent studies shown in this book reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. In some sense, frustrated systems provide an excellent testing ground for approximations and theories. Experimentally, more and more frustrated materials are discovered with interesting properties for applications.

This book represents a simple idea with profound implications for science and philosophy. It develops a new foundation at both a popular and technological level of current fundamental theories.

Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.

How can we predict and explain the phenomena of nature? What are the limits to this knowledge process? The central issues of prediction, explanation, and mathematical modeling, which underlie all scientific activity, were the focus of a conference organized by the Swedish Council for the Planning and Coordination of Research, held at the Abisko Research Station in May of 1989. At this forum, a select group of internationally known scientists in physics, chemistry, biology, economics, sociology and mathematics discussed and debated the ways in which prediction and explanation interact with mathematical modeling in their respective areas of expertise. Beyond Belief is the result of this forum, consisting of 11 chapters written specifically for this volume. The multiple themes of randomness, uncertainty, prediction and explanation are presented using (as vehicles) several topical areas from modern science, such as morphogenetic fields, Boscovich covariance, and atmospheric variability. This multidisciplinary examination of the foundational issues of modern scientific thought and methodology will offer stimulating reading for a very broad scientific audience.

This course includes an overview of current theory and practice. The paperback edition offers current and prospective teachers of English a comprehensive treatment of pronunciation pedagogy, drawing on current theory and practice. The text provides an overview of teaching issues from the perspective of different methodologies and second language acquisition research. It has a thorough grounding in the sound system of North American English, and contains insights into how this sound system intersects with listening, morphology, and spelling. It also contains diagnostic tools, assessment measures, and suggestions for syllabus design. Discussion questions encourage readers to draw on their personal language learning/teaching experiences as they assimilate the contents of each chapter. Follow-up exercises guide teachers in developing a range of classroom activities within a communicative framework.