Differential Topology And Geometry With Applications To Physics

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Differential Topology and Geometry with Applications to Physics

Eduardo Nahmad-Achar
Differential Topology and Geometry with Applications to Physics Book PDF

Author : Eduardo Nahmad-Achar
Publisher : Unknown
Page : 0 pages
File Size : 44,8 Mb
Release : 2018
Category : Geometry, Differential
ISBN : 0750320729

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Differential Topology and Geometry with Applications to Physics by Eduardo Nahmad-Achar Pdf

"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.

Differential Topology and Geometry with Applications to Physics

Eduardo Nahmad-Achar
Differential Topology and Geometry with Applications to Physics Book PDF

Author : Eduardo Nahmad-Achar
Publisher : Programme: Iop Expanding Physi
Page : 200 pages
File Size : 44,8 Mb
Release : 2018-12-21
Category : Mathematics
ISBN : 0750320702

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Differential Topology and Geometry with Applications to Physics by Eduardo Nahmad-Achar Pdf

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.

Topology and Geometry for Physics

Helmut Eschrig
Topology and Geometry for Physics Book PDF

Author : Helmut Eschrig
Publisher : Springer
Page : 397 pages
File Size : 50,7 Mb
Release : 2011-01-26
Category : Science
ISBN : 9783642147005

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Topology and Geometry for Physics by Helmut Eschrig Pdf

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.

An Introduction To Differential Geometry And Topology In Mathematical Physics

Wang Rong,Chen Yue
An Introduction To Differential Geometry And Topology In Mathematical Physics Book PDF

Author : Wang Rong,Chen Yue
Publisher : World Scientific
Page : 222 pages
File Size : 50,5 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.

Differential Topology and Quantum Field Theory

Charles Nash
Differential Topology and Quantum Field Theory Book PDF

Author : Charles Nash
Publisher : Elsevier
Page : 404 pages
File Size : 46,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0125140762

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Differential Topology and Quantum Field Theory by Charles Nash Pdf

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. Treats differential geometry, differential topology, and quantum field theory Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory Tackles problems of quantum field theory using differential topology as a tool

Differential Geometry with Applications to Mechanics and Physics

Yves Talpaert
Differential Geometry with Applications to Mechanics and Physics Book PDF

Author : Yves Talpaert
Publisher : CRC Press
Page : 480 pages
File Size : 40,7 Mb
Release : 2000-09-12
Category : Mathematics
ISBN : 0824703855

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Differential Geometry with Applications to Mechanics and Physics by Yves Talpaert Pdf

An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Geometry, Topology and Physics

Mikio Nakahara
Geometry Topology and Physics Book PDF

Author : Mikio Nakahara
Publisher : Taylor & Francis
Page : 596 pages
File Size : 45,5 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.

Topology and Geometry for Physicists

Charles Nash,Siddhartha Sen
Topology and Geometry for Physicists Book PDF

Author : Charles Nash,Siddhartha Sen
Publisher : Courier Corporation
Page : 302 pages
File Size : 41,9 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.

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics

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

Author : Antonio Sergio Teixeira Pires
Publisher : Morgan & Claypool Publishers
Page : 171 pages
File Size : 47,9 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.

Differential Geometry and Mathematical Physics

Gerd Rudolph,Matthias Schmidt
Differential Geometry and Mathematical Physics Book PDF

Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 47,8 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457

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Differential Geometry and Mathematical Physics by Gerd Rudolph,Matthias Schmidt Pdf

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Exotic Smoothness and Physics

Torsten Asselmeyer-Maluga
Exotic Smoothness and Physics Book PDF

Author : Torsten Asselmeyer-Maluga
Publisher : World Scientific
Page : 339 pages
File Size : 48,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812706669

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Exotic Smoothness and Physics by Torsten Asselmeyer-Maluga Pdf

The recent revolution in differential topology related to the discovery of non-standard (OC exoticOCO) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit OCo but now shown to be incorrect OCo assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, EinsteinOCOs relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models."

Differential Equations on Manifolds and Mathematical Physics

Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Differential Equations on Manifolds and Mathematical Physics Book PDF

Author : Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang
Publisher : Springer Nature
Page : 349 pages
File Size : 43,7 Mb
Release : 2022-01-21
Category : Mathematics
ISBN : 9783030373269

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Differential Equations on Manifolds and Mathematical Physics by Vladimir M. Manuilov,Alexander S. Mishchenko,Vladimir E. Nazaikinskii,Bert-Wolfgang Schulze,Weiping Zhang Pdf

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

Differential Geometry and Topology

Keith Burns,Marian Gidea
Differential Geometry and Topology Book PDF

Author : Keith Burns,Marian Gidea
Publisher : CRC Press
Page : 403 pages
File Size : 41,7 Mb
Release : 2005-05-27
Category : Mathematics
ISBN : 9781420057539

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Differential Geometry and Topology by Keith Burns,Marian Gidea Pdf

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics

Algebraic Topology Via Differential Geometry

M. Karoubi,C. Leruste
Algebraic Topology Via Differential Geometry Book PDF

Author : M. Karoubi,C. Leruste
Publisher : Cambridge University Press
Page : 380 pages
File Size : 55,7 Mb
Release : 1987
Category : Mathematics
ISBN : 0521317142

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Algebraic Topology Via Differential Geometry by M. Karoubi,C. Leruste Pdf

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Applications of Contact Geometry and Topology in Physics

Arkady Leonidovich Kholodenko
Applications of Contact Geometry and Topology in Physics Book PDF

Author : Arkady Leonidovich Kholodenko
Publisher : World Scientific
Page : 492 pages
File Size : 53,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814412094

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Applications of Contact Geometry and Topology in Physics by Arkady Leonidovich Kholodenko Pdf

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.