Geometry And Physics
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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.
Geometry And Physics
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-17
Geometry And Physics written by Jürgen Jost 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 2009-08-17 with Mathematics categories.
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
The Geometry And Physics Of Knots
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Author : Michael Francis Atiyah
language : en
Publisher: Cambridge University Press
Release Date : 1990-08-23
The Geometry And Physics Of Knots written by Michael Francis Atiyah and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-23 with Mathematics categories.
These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Geometry And Physics
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Author : Jørgen Ellegaard Andersen
language : en
Publisher: Oxford University Press, USA
Release Date : 2018
Geometry And Physics written by Jørgen Ellegaard Andersen and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
The Geometry Of Physics
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Author : Frankel Theodore
language : en
Publisher: 清华大学出版社有限公司
Release Date : 2005
The Geometry Of Physics written by Frankel Theodore and has been published by 清华大学出版社有限公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Geometry, Differential categories.
Nonlinear Partial Differential Equations In Geometry And Physics
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Author : Garth Baker
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Nonlinear Partial Differential Equations In Geometry And Physics written by Garth Baker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Geometry And Physics Volume 2
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Author : Jørgen Ellegaard Andersen
language : en
Publisher: Oxford University Press
Release Date : 2018-10-18
Geometry And Physics Volume 2 written by Jørgen Ellegaard Andersen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Mathematics categories.
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
Noncommutative Geometry And Physics 2005
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Author : Ursula Carow-Watamura
language : en
Publisher: World Scientific
Release Date : 2007
Noncommutative Geometry And Physics 2005 written by Ursula Carow-Watamura and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space?time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.
Differential Geometry And Physics
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Author : Mo-Lin Ge
language : en
Publisher: World Scientific
Release Date : 2006
Differential Geometry And Physics written by Mo-Lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.
Special Metrics And Supersymmetry
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Author : Luis Carlos de Andrés
language : en
Publisher: American Institute of Physics
Release Date : 2009-02-25
Special Metrics And Supersymmetry written by Luis Carlos de Andrés and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-25 with Mathematics categories.
All papers have been peer-reviewed. This volume includes the contributions to the International Workshop on Geometry and Physics: Special Metrics and Supersymmetry, held at the University of the Basque Country, Bilbao (Spain), from May 29 to 31, 2008. The topics covered by the volume deal with leading aspects of algebraic and differential geometry with special emphasis to their potential applications in supersymmetry and string theories. The areas covered by the proceedings are algebraic geometry, differential geometry and mathematical physics. In greater detail, they cover outstanding topics such as homological mirror symmetry, generalized Hodge theory, coassociative submanifolds, special geometric structures, geometric structures, Killing spinors, torsion geometry, string theory, supersymmetry and T-duality, among others.