A Brief Introduction To Topology And Differential Geometry In Condensed Matter Physics Second Edition
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Author | : Antonio Sergio Teixeira Pires |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 171 |
Release | : 2019-03-21 |
Genre | : Science |
ISBN | : 1643273744 |
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 | : |
Total Pages | : 0 |
Release | : 1901 |
Genre | : |
ISBN | : 9781643273730 |
Author | : Mikio Nakahara |
Publisher | : Taylor & Francis |
Total Pages | : 596 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1420056948 |
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 | : Charles Nash |
Publisher | : Courier Corporation |
Total Pages | : 302 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0486318362 |
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 | : Eike Bick |
Publisher | : Springer Science & Business Media |
Total Pages | : 380 |
Release | : 2005-01-18 |
Genre | : Mathematics |
ISBN | : 9783540231257 |
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 | : Eduardo Nahmad-Achar |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : Geometry, Differential |
ISBN | : 9780750320719 |
"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.
Author | : Eike Bick |
Publisher | : Springer |
Total Pages | : 362 |
Release | : 2009-09-02 |
Genre | : Science |
ISBN | : 9783540803980 |
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 | : David S Simon |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 130 |
Release | : 2018-11-06 |
Genre | : Science |
ISBN | : 1643272349 |
Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
Author | : J. F. Sadoc |
Publisher | : World Scientific |
Total Pages | : 318 |
Release | : 1990 |
Genre | : Science |
ISBN | : 9789810200893 |
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 | : Wang Rong |
Publisher | : World Scientific |
Total Pages | : 222 |
Release | : 1999-01-18 |
Genre | : Mathematics |
ISBN | : 9814495808 |
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.