Topology And Geometry For Physics

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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.

Geometry Topology And Physics Second Edition

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Author : Mikio Nakahara
language : en
Publisher: CRC Press
Release Date : 2003-06-04

Geometry Topology And Physics Second Edition written by Mikio Nakahara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-04 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.

Topology And Geometry In Physics

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Author : Eike Bick
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-18

Topology And Geometry In Physics written by Eike Bick 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 2005-01-18 with Mathematics categories.

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.

Topology And Geometry For Physics

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Author : Helmut Eschrig
language : en
Publisher: Springer
Release Date : 2011-01-26

Topology And Geometry For Physics written by Helmut Eschrig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-26 with Science categories.

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.

Applications Of Contact Geometry And Topology In Physics

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Author : Arkady L Kholodenko
language : en
Publisher: World Scientific
Release Date : 2013-05-03

Applications Of Contact Geometry And Topology In Physics written by Arkady L Kholodenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-03 with Mathematics categories.

Although contact geometry and topology is briefly discussed in V I Arnol'd's book “Mathematical Methods of Classical Mechanics ”(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges “An Introduction to Contact Topology” (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph “Contact Geometry and Nonlinear Differential Equations” (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.

Topology And Geometry In Physics

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Author : Eike Bick
language : en
Publisher: Springer
Release Date : 2009-09-02

Topology And Geometry In Physics written by Eike Bick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Science categories.

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.

Modern Differential Geometry For Physicists

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Author : Chris J. Isham
language : en
Publisher: Allied Publishers
Release Date : 2002

Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.

Topology For Physicists

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Author : Albert S. Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-16

Topology For Physicists written by Albert S. Schwarz 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 1996-07-16 with Mathematics categories.

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.

Differential Topology And Geometry With Applications To Physics

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Author : Eduardo Nahmad-Achar
language : en
Publisher: Institute of Physics Publishing
Release Date : 2018-12-21

Differential Topology And Geometry With Applications To Physics written by Eduardo Nahmad-Achar and has been published by Institute of Physics Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-21 with Mathematics categories.

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.

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.