Topology and Geometry for Physicists - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology and Geometry for Physicists write by Charles Nash. This book was released on 2013-08-16. Topology and Geometry for Physicists available in PDF, EPUB and Kindle. Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
Topology and Geometry for Physics
Topology and Geometry for Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology and Geometry for Physics write by Helmut Eschrig. This book was released on 2011-01-26. Topology and Geometry for Physics available in PDF, EPUB and Kindle. A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.
Geometry, Topology and Physics
Geometry, Topology and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry, Topology and Physics write by Mikio Nakahara. This book was released on 2018-10-03. Geometry, Topology and Physics available in PDF, EPUB and Kindle. 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.
Differential Topology and Geometry with Applications to Physics
Differential Topology and Geometry with Applications to Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Topology and Geometry with Applications to Physics write by Eduardo Nahmad-Achar. This book was released on 2018. Differential Topology and Geometry with Applications to Physics available in PDF, EPUB and Kindle. "Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics." -- Prové de l'editor.
Topology, Geometry, and Gauge Fields
Topology, Geometry, and Gauge Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology, Geometry, and Gauge Fields write by Gregory L. Naber. This book was released on 2013-04-17. Topology, Geometry, and Gauge Fields available in PDF, EPUB and Kindle. Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
