Download or read book Riemann Topology and Physics written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2009-06-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.
Download or read book Riemann Topology and Physics written by Michael Monastyrsky and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soviet citizens can buy Monastyrsky's biography of Riemann for eleven kopeks. This translated edition will cost considerably more, but it is still good value for the money. And we get Monastyrsky's monograph on topological methods in the bargain. It was a good idea of Birkhiiuser Boston to publish the two translations in one volume. The economics of publishing in a capitalist country make it impossible for us to produce the small cheap paperback booklets, low in quality of paper and high in quality of scholarship, at which the Soviet publishing industry excels. Monastyrsky's two booklets are out standing examples of the genre. By putting them together, Birkhiiuser has enabled them to fit into the Western book-marketing system. The two booklets were written separately and each is complete in itself, but they complement each other beautifully. The Riemann biography is short and terse, like Riemann's own writings. It describes in few words and fewer equations the revolutionary ideas which Riemann brought into mathematics and physics a hundred and twenty years ago. The topological methods booklet describes how some of these same ideas, after lying dormant for a century, found new and fruitful applications in the physics of our own time.
Download or read book Riemann Topology and Physics written by Mikhail Ilʹich Monastyrskiĭ and published by Birkhauser. This book was released on 1999 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topology And Physics written by Chen Ning Yang and published by World Scientific. This book was released on 2019-01-09 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
Download or read book From Riemann to Differential Geometry and Relativity written by Lizhen Ji and published by Springer. This book was released on 2017-10-03 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Download or read book The Concept of a Riemann Surface written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-12-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
Download or read book Riemannian Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Download or read book Geometry Topology and Physics written by Mikio Nakahara and published by Taylor & Francis. This book was released on 2018-10-03 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
Download or read book Riemann Surfaces and Algebraic Curves written by Renzo Cavalieri and published by Cambridge University Press. This book was released on 2016-09-26 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Download or read book Riemann Surfaces written by Simon Donaldson and published by Oxford University Press. This book was released on 2011-03-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.
Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho and published by Springer. This book was released on 2014-07-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
Download or read book Differential Manifolds and Theoretical Physics written by and published by Academic Press. This book was released on 1985-05-24 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Manifolds and Theoretical Physics
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 The Geometry of Physics written by Theodore Frankel and published by Cambridge University Press. This book was released on 2011-11-03 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady Leonidovich Kholodenko and published by World Scientific. This book was released on 2013 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
Download or read book Topology and Geometry written by Glen E. Bredon and published by Springer Science & Business Media. This book was released on 1993-06-24 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
