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A New Spin On Mathematics
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Book Synopsis Spin Glasses: A Challenge for Mathematicians by : Michel Talagrand
Download or read book Spin Glasses: A Challenge for Mathematicians written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2003-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.
Download or read book Spin Geometry written by H. Blaine Lawson and published by Princeton University Press. This book was released on 2016-06-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Book Synopsis Putting A New Spin on Groups by : Bud A. McClure
Download or read book Putting A New Spin on Groups written by Bud A. McClure and published by Psychology Press. This book was released on 2005-01-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Putting a New Spin on Groups: The Science of Chaos, Second Edition continues to challenge orthodoxy and static ideas about small group dynamics. A primary goal is to offer an alternative model of group development that addresses three factors: *The model integrates old ideas from previous models of group development with new concepts from chaos theory and the work of Arthur Young. *The book emphasizes the importance of conflict in group development and recognizes that group growth--while progressive--is neither linear or unidimensional. *Particular attention is focused on how groups change, evolve, and mature. In addition, this book highlights certain group phenomena that have been given only cursory attention in many group textbooks, including women in authority, group metaphors, regressive groups, and the transpersonal potential of small groups. This book has been revised in response to feedback from reviewers and colleagues and includes new ideas, applications of chaos theory in social sciences, and thinking about group behavior. It is an intellectually challenging read with just the right amount of world application.
Book Synopsis The Theory of Spinors by : Élie Cartan
Download or read book The Theory of Spinors written by Élie Cartan and published by Courier Corporation. This book was released on 2012-04-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
Book Synopsis Spin Glasses and Complexity by : Daniel L. Stein
Download or read book Spin Glasses and Complexity written by Daniel L. Stein and published by Princeton University Press. This book was released on 2013-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Spin Glasses and Complexity 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. It 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, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.
Book Synopsis Conformal Groups in Geometry and Spin Structures by : Pierre Anglès
Download or read book Conformal Groups in Geometry and Spin Structures written by Pierre Anglès and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
Book Synopsis A New Kind of Science by : Stephen Wolfram
Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
Book Synopsis Perspectives on Spin Glasses by : Pierluigi Contucci
Download or read book Perspectives on Spin Glasses written by Pierluigi Contucci and published by Cambridge University Press. This book was released on 2013 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting and developing the theory of spin glasses for mathematical physicists and probabilists working in disordered systems.
Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : Rafal Ablamowicz
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Book Synopsis Rotations, Quaternions, and Double Groups by : Simon L. Altmann
Download or read book Rotations, Quaternions, and Double Groups written by Simon L. Altmann and published by Courier Corporation. This book was released on 2013-04-09 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Book Synopsis Quantum Mechanics for Mathematicians by : Leon Armenovich Takhtadzhi͡an
Download or read book Quantum Mechanics for Mathematicians written by Leon Armenovich Takhtadzhi͡an and published by American Mathematical Soc.. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.
Book Synopsis Superintegrability in Classical and Quantum Systems by : Piergiulio Tempesta
Download or read book Superintegrability in Classical and Quantum Systems written by Piergiulio Tempesta and published by American Mathematical Soc.. This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Book Synopsis Dirac Operators in Riemannian Geometry by : Thomas Friedrich
Download or read book Dirac Operators in Riemannian Geometry written by Thomas Friedrich and published by American Mathematical Soc.. This book was released on 2000 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and $\textrm{spin}mathbb{C}$ structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.
Download or read book Spin written by Lamar Giles and published by Scholastic Inc.. This book was released on 2019-01-29 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even in murder, the music lives on. When rising star Paris Secord (aka DJ ParSec) is found dead on her turntables, it sends the local music scene reeling. No one is feeling that grief more than her shunned pre-fame best friend, Kya, and ParSec's chief groupie, Fuse -- two sworn enemies who happened to be the ones who discovered her body. The police have few leads, and when the trail quickly turns cold, the authorities don't seem to be pushing too hard to investigate further. But nobody counted on Paris's deeply loyal fans, ParSec Nation, or the outrage that would drive Fuse and Kya to work together. As ParSec Nation takes to social media and the streets in their crusade for justice, Fuse and Kya start digging into Paris's past, stumbling across a deadly secret. With new info comes new motives. New suspects. And a fandom that will stop at nothing in their obsessive quest for answers, not even murder...
Download or read book Spin Glasses written by Erwin Bolthausen and published by Springer. This book was released on 2007-01-11 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Book Synopsis An Introduction to the Theory of Spin Glasses and Neural Networks by : Viktor Dotsenko
Download or read book An Introduction to the Theory of Spin Glasses and Neural Networks written by Viktor Dotsenko and published by World Scientific. This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to describe in simple terms the new area of statistical mechanics known as spin-glasses, encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Next, the 'magic' of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be studied in the laboratory. The final chapters of the book are devoted to statistical models of neural networks.The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.
Book Synopsis Mathematical Aspects of Spin Glasses and Neural Networks by : Anton Bovier
Download or read book Mathematical Aspects of Spin Glasses and Neural Networks written by Anton Bovier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:
