Solitons Instantons And Twistors
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Solitons Instantons And Twistors
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Author : Maciej Dunajski
language : en
Publisher: OUP Oxford
Release Date : 2009-12-10
Solitons Instantons And Twistors written by Maciej Dunajski and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.
A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.
Solitons Instantons And Twistors
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Author : Professor of Mathematical Physics Maciej Dunajski
language : en
Publisher: Oxford University Press
Release Date : 2024-07-15
Solitons Instantons And Twistors written by Professor of Mathematical Physics Maciej Dunajski 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 2024-07-15 with Mathematics categories.
The book provides a self-contained and accessible introduction to integrable systems. It starts with an introduction to integrability of ordinary and partial differential equations, and goes on to explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations.
Solitons Instantons And Twistors
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Author : Maciej Dunajski
language : en
Publisher: OUP Oxford
Release Date : 2009-12-10
Solitons Instantons And Twistors written by Maciej Dunajski and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
Geometry A Very Short Introduction
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Author : Maciej Dunajski
language : en
Publisher: Oxford University Press
Release Date : 2022-01-27
Geometry A Very Short Introduction written by Maciej Dunajski 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 2022-01-27 with Geometry categories.
The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics.This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics,Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art.Very Short Introductions: Brilliant, Sharp, InspiringABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.
Solitons And Instantons
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Author : R. Rajaraman
language : en
Publisher:
Release Date : 1987
Solitons And Instantons written by R. Rajaraman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Algebraic Models In Geometry
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Author : Yves Félix
language : en
Publisher: Oxford University Press
Release Date : 2008
Algebraic Models In Geometry written by Yves Félix 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 2008 with Mathematics categories.
A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.
An Introduction To Algebraic Geometry And Algebraic Groups
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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2013-03-14
An Introduction To Algebraic Geometry And Algebraic Groups written by Meinolf Geck 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 2013-03-14 with Mathematics categories.
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Quantum Mechanics
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Author : Kenichi Konishi
language : en
Publisher: Oxford University Press
Release Date : 2009-03-05
Quantum Mechanics written by Kenichi Konishi 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 2009-03-05 with Mathematics categories.
A modern and comprehensive textbook intended to correct the lack of such a text in times of the ever-increasing importance of the subject in contemporary science, technology, and everyday life. With its clear pedagogical presentation and with many examples and solved problems it is useful for physics students, researchers and teachers alike.
Algebraic Geometry And Arithmetic Curves
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Author : Qing Liu
language : en
Publisher: Oxford University Press
Release Date : 2006-06-29
Algebraic Geometry And Arithmetic Curves written by Qing Liu 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 2006-06-29 with Mathematics categories.
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Integrable Systems
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Author : N. J. Hitchin
language : en
Publisher: OUP Oxford
Release Date : 2013-03-14
Integrable Systems written by N. J. Hitchin and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do we recognize an integrable system? His own contribution then develops connections with algebraic geometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles. Graeme Segal takes the Kortewegde Vries and nonlinear Schrödinger equations as central examples, and explores the mathematical structures underlying the inverse scattering transform. He explains the roles of loop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and the self-dual Yang-Mills equations, and describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.