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Published by Springer International Publishing AG, Cham, 2024
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Hardcover. Condition: new. Hardcover. This textbook is based on the author's lecture notes held at Qiuzhen College, Tsinghua University, Beijing, renowned for its rapid scientific growth of its excellent students. The book offers a remarkable combination of characteristics that are both exceptional and seemingly contradictory. It is designed to be entirely self-contained, starting from the basics and building a strong foundation in geometric and algebraic tools. Simultaneously, topics are infused with mathematical elegance and profundity, employing contemporary language and techniques. From a physicist's perspective, the content delves deeply into the physical aspects, emphasizing the underlying principles. This book bridges the gap between students and cutting-edge research, with a special focus on symplectic geometry, integrability, and recent developments in the field. It is designed to engage and captivate the reader. A conscious selection of topics ensures a more relevant and contemporary approach compared to traditional textbooks. The book addresses common misconceptions, offering clarity and precision. In its quest for brevity, this book is tailored for a one-semester course, offering a comprehensive and concise resource. The author's dedication is evident throughout this volume, encapsulating these goals within roughly 300 pages. This textbook is based on the author's lecture notes held at Qiuzhen College, Tsinghua University, Beijing, renowned for its rapid scientific growth of its excellent students. This book bridges the gap between students and cutting-edge research, with a special focus on symplectic geometry, integrability, and recent developments in the field. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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Published by Cambridge University Press, 2015
ISBN 10: 1107053811 ISBN 13: 9781107053816
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ISBN 10: 1107053811 ISBN 13: 9781107053816
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Published by Springer International Publishing AG, Cham, 2024
ISBN 10: 3031678737 ISBN 13: 9783031678738
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Hardcover. Condition: new. Hardcover. This textbook is based on lecture notes that the author delivered at Qiuzhen College (Tsinghua University), a Chinese institution known for its exceptionally talented mathematics students. The book's intended audience shapes its character. It introduces Statistical Mechanics from the ground up, offering a fully self-contained presentation that aims for mathematical precision. It distinguishes rigorous results from controlled approximations and provides physical insights into phenomena.Despite its concise nature (suited for a one-semester basic course), this book covers several topics typically not found in introductory texts. These include Shannon's information-theoretic interpretation of entropy, the gauge approach to order-disorder duality in the Ising model, the Yang-Lee theory, and the quantum dissipation-fluctuation theorem. Additionally, it explores frustrated and quenched systems, including an introduction to the celebrated Parisi solution of the Sherrington-Kirkpatrick model of spin glasses.The path integral formalism is extensively discussed from various perspectives to suit different applications. Chapter 2 approaches path integrals through the Feynman-Kac formula and second quantization. In Chapter 5, they are examined within the context of effective field theories like Landau-Ginzburg theory, while Chapter 6 delves into their connection with Brownian motion, Langevin stochastic differential equations, and Fokker-Planck diffusion PDEs. The book also explores the relationship between stochastic processes and supersymmetry.Various techniques for computing path integrals, especially functional determinants, are introduced throughout the relevant chapters, offering the most suitable computational tools for each application. In Chapter 5, they are examined within the context of effective field theories like Landau-Ginzburg theory, while Chapter 6 delves into their connection with Brownian motion, Langevin stochastic differential equations, and Fokker-Planck diffusion PDEs. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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Published by Cambridge University Press, 2015
ISBN 10: 1107053811 ISBN 13: 9781107053816
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Published by Cambridge University Press, 2015
ISBN 10: 1107053811 ISBN 13: 9781107053816
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