A Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics
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A Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics
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Author : Antonio Sergio Teixeira Pires
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2019-03-21
A Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics written by Antonio Sergio Teixeira Pires and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Science categories.
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
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Author : Pires Antonio Sergio Teixeira
language : en
Publisher:
Release Date : 1901
Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics written by Pires Antonio Sergio Teixeira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1901 with categories.
Many Body Physics Topology And Geometry
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Author : Siddhartha Sen
language : en
Publisher: World Scientific
Release Date : 2015-06-15
Many Body Physics Topology And Geometry written by Siddhartha Sen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-15 with Science categories.
The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics. With this aim, a brief intuitive introduction to many-body theory is given as a powerful qualitative tool for understanding complex systems. The important emergent concept of a quasiparticle is then introduced as a way to reduce a many-body problem to a single particle quantum problem. Examples of quasiparticles in graphene, superconductors, superfluids and in a topological insulator on a superconductor are discussed. The mathematical idea of self-adjoint extension, which allows short distance information to be included in an effective long distance theory through boundary conditions, is introduced through simple examples and then applied extensively to analyse and predict new physical consequences for graphene. The mathematical discipline of topology is introduced in an intuitive way and is then combined with the methods of differential geometry to show how the emergence of gapless states can be understood. Practical ways of carrying out topological calculations are described. Contents:OverviewMany-Body TheoryTopology and GeometryBoundary Conditions and Self-Adjoint ExtensionsElectronic Properties of Graphene Readership: Graduate students and researchers in condensed matter physics and mathematical physics. Key Features:Topics are of current interest, e.g. graphene, topological insulators, Majorana fermionsIs self-contained and provides all the background material necessary to understand the physical or mathematical concepts discussedPractical ways of using topology, self-adjoint extensions as well as ways of making qualitative estimates in physics are explained and then illustrated by examplesKeywords:Condensed Matter Physics;Topology;Differential Geometry;Many-Body Problem;Graphene;Self-Adjoint Extensions;K-Theory;Quasiparticles;Superconductivity;Superfluidity;Topological Insulator;Mathematical Physics
Geometry Topology And Physics
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Author : Mikio Nakahara
language : en
Publisher: Taylor & Francis
Release Date : 2018-10-03
Geometry Topology And Physics written by Mikio Nakahara and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
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.
An Introduction To Differential Geometry And Topology In Mathematical Physics
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Author : Wang Rong
language : en
Publisher: World Scientific
Release Date : 1999-01-18
An Introduction To Differential Geometry And Topology In Mathematical Physics written by Wang Rong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-18 with Mathematics categories.
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.
Topology And Geometry For Physicists
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Author : Charles Nash
language : en
Publisher: Courier Corporation
Release Date : 2013-08-16
Topology And Geometry For Physicists written by Charles Nash and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.
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.
Introduction To Topology Differential Geometry And Group Theory For Physicists
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Author : Sunil Mukhi
language : en
Publisher:
Release Date : 1990
Introduction To Topology Differential Geometry And Group Theory For Physicists written by Sunil Mukhi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Differential topology categories.
Topology In Condensed Matter An Introduction
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Author : Miguel A N Araujo
language : en
Publisher: World Scientific
Release Date : 2021-05-19
Topology In Condensed Matter An Introduction written by Miguel A N Araujo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Science categories.
This text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems. It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter. In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems. It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems.This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals. It includes all the mathematical background required for the subject. There are very few books with such a coverage in the market.
Topology In Condensed Matter
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Author : Michael I. Monastyrsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-04
Topology In Condensed Matter written by Michael I. Monastyrsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-04 with Science categories.
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
Topology And Geometry For Physicists
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Author : Charles Nash
language : en
Publisher: Elsevier
Release Date : 1988-01-04
Topology And Geometry For Physicists written by Charles Nash and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-04 with Mathematics categories.
Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book. An obvious omission here is general relativity--we apologize for this. We originally intended to discuss general relativity. However, both the need to keep the size of the book within the reasonable limits and the fact that accounts of the topology and geometry of relativity are already available, for example, in The Large Scale Structure of Space-Time by S. Hawking and G. Ellis, made us reluctantly decide to omit this topic.