A Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics

Author : Antonio Sergio Teixeira Pires
Publisher : Morgan & Claypool Publishers
Page : 171 pages
File Size : 53,8 Mb
Release : 2019-03-21
Category : Science
ISBN : 9781643273747

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A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by Antonio Sergio Teixeira Pires Pdf

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.

Author : Pires Antonio Sergio Teixeira
Publisher : Unknown
Page : 0 pages
File Size : 40,6 Mb
Release : 1901
Category : Electronic
ISBN : 1643273736

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Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by Pires Antonio Sergio Teixeira Pdf

Author : Mikio Nakahara
Publisher : Taylor & Francis
Page : 596 pages
File Size : 46,5 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781420056945

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Geometry, Topology and Physics by Mikio Nakahara Pdf

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.

Author : Siddhartha Sen,Kumar Sankar Gupta
Publisher : World Scientific
Page : 220 pages
File Size : 55,5 Mb
Release : 2015-06-15
Category : Science
ISBN : 9789814678186

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Many-Body Physics, Topology and Geometry by Siddhartha Sen,Kumar Sankar Gupta Pdf

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

Author : Wang Rong,Chen Yue
Publisher : World Scientific
Page : 222 pages
File Size : 44,5 Mb
Release : 1999-01-18
Category : Mathematics
ISBN : 9789814495806

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An Introduction To Differential Geometry And Topology In Mathematical Physics by Wang Rong,Chen Yue Pdf

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.

Author : Eike Bick
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 55,9 Mb
Release : 2005-01-18
Category : Mathematics
ISBN : 3540231250

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Topology and Geometry in Physics by Eike Bick Pdf

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Author : Charles Nash,Siddhartha Sen
Publisher : Courier Corporation
Page : 302 pages
File Size : 43,5 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318363

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Topology and Geometry for Physicists by Charles Nash,Siddhartha Sen Pdf

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.

Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 44,7 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169

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Modern Differential Geometry for Physicists by Chris J. Isham Pdf

Author : Eike Bick,Frank Daniel Steffen
Publisher : Springer
Page : 362 pages
File Size : 43,5 Mb
Release : 2009-09-02
Category : Science
ISBN : 354080398X

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Topology and Geometry in Physics by Eike Bick,Frank Daniel Steffen Pdf

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Author : Somendra Mohan Bhattacharjee,Mahan Mj,Abhijit Bandyopadhyay
Publisher : Springer
Page : 507 pages
File Size : 42,8 Mb
Release : 2017-12-20
Category : Science
ISBN : 9789811068416

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Topology and Condensed Matter Physics by Somendra Mohan Bhattacharjee,Mahan Mj,Abhijit Bandyopadhyay Pdf

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.

Author : J. F. Sadoc
Publisher : World Scientific
Page : 318 pages
File Size : 47,8 Mb
Release : 1990
Category : Science
ISBN : 9810200897

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Geometry in Condensed Matter Physics by J. F. Sadoc Pdf

The subject of geometry has become an important ingredient in condensed matter physics. It appears not only to describe, but also to explain structures and their properties. There are two aspects to using geometry: the visual and intuitive understanding, which fosters an immediate grasp of the objects one studies, and the abstract tendency so well developed in the Riemannian manifold theory. Both aspects contribute to the same understanding when they are applied to the main problems occurring in condensed matter sciences. Sophisticated structures found in nature appear naturally as the result of simple constraints which are presented in geometrical terms. Blue phases, amorphous and glassy materials, Frank and Kasper Metals, quasi-crystals are approached in their complexity, using the simple principles of geometry. The relation between biology and liquid crystal sciences, the physics of membranes is a fundamental aspect presented in this book.

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 54,5 Mb
Release : 2006-02-04
Category : Science
ISBN : 9783540312642

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Topology in Condensed Matter by Michael I. Monastyrsky Pdf

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.

Author : Sunil Mukhi,N. Mukunda
Publisher : Unknown
Page : 210 pages
File Size : 45,7 Mb
Release : 1990
Category : Differential topology
ISBN : 8122402631

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Introduction to Topology, Differential Geometry and Group Theory for Physicists by Sunil Mukhi,N. Mukunda Pdf

Author : Miguel A N Araujo,Pedro Sacramento
Publisher : World Scientific
Page : 276 pages
File Size : 54,8 Mb
Release : 2021-05-19
Category : Science
ISBN : 9789811237232

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Topology In Condensed Matter: An Introduction by Miguel A N Araujo,Pedro Sacramento Pdf

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.

Author : M. Monastyrsky
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 55,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489924032

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Topology of Gauge Fields and Condensed Matter by M. Monastyrsky Pdf

''Intended mainly for physicists and mathematicians...its high quality will definitely attract a wider audience.'' ---Computational Mathematics and Mathematical Physics This work acquaints the physicist with the mathematical principles of algebraic topology, group theory, and differential geometry, as applicable to research in field theory and the theory of condensed matter. Emphasis is placed on the topological structure of monopole and instanton solution to the Yang-Mills equations, the description of phases in superfluid 3He, and the topology of singular solutions in 3He and liquid crystals.