A Brief Introduction to Topology and Differential Geometry in Condensed Matter 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 A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics write by Antonio Sergio Teixeira Pires. This book was released on 2019-03-21. A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics available in PDF, EPUB and Kindle. In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.
Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics
Brief Introduction to Topology and Differential Geometry in Condensed Matter 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 Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics write by Pires Antonio Sergio Teixeira. This book was released on 1901. Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics available in PDF, EPUB and Kindle.
Topology and Geometry for Physicists
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.
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.
Topology and Condensed Matter Physics
Topology and Condensed Matter 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 Condensed Matter Physics write by Somendra Mohan Bhattacharjee. This book was released on 2017-12-20. Topology and Condensed Matter Physics available in PDF, EPUB and Kindle. This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail.
