Solitons Instantons And Twistors
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Solitons Instantons And Twistors
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Author : Maciej Dunajski
language : en
Publisher: Oxford University Press, USA
Release Date : 2010
Solitons Instantons And Twistors written by Maciej Dunajski 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 2010 with Language Arts & Disciplines 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:
Release Date : 2023
Solitons Instantons And Twistors written by Maciej Dunajski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Geometry, Differential 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 : 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.
An Introduction To Module Theory
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Author : Ibrahim Assem
language : en
Publisher: Oxford University Press
Release Date : 2024-11-21
An Introduction To Module Theory written by Ibrahim Assem 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 2024-11-21 with Mathematics categories.
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work. Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.
Noncommutative Measures And Lp And Orlicz Spaces With Applications To Quantum Physics
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Author : Stanisław Goldstein
language : en
Publisher: Oxford University Press
Release Date : 2025-06-19
Noncommutative Measures And Lp And Orlicz Spaces With Applications To Quantum Physics written by Stanisław Goldstein 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 2025-06-19 with Mathematics categories.
The theory of noncommutative Haagerup Lp and Orlicz spaces is an important tool in both Quantum Harmonic Analysis and Mathematical Physics. Indeed, noncommutativity is arguably the raison-d'être of the Heisenberg approach to quantum mechanics. Just as classical analysis formed the foundation for classical mechanics, a mature response to the challenges posed by quantum mechanics (from the Heisenberg perspective) similarly needs to be built on a well-developed foundation of noncommutative analysis. In the passage from the classical to the quantum setting, functions get replaced with (possibly noncommuting) operators. Von Neumann himself realised early on that some sort of noncommutative integral calculus tailored to this setting is therefore needed to meet this challenge. This book seeks to help address this need. The noncommutative Orlicz spaces presented here help in dealing with observable quantities and entropy. Goldstein and Labuschagne provide a detailed account of the current theories in a way that is useful and accessible to a wide range of readers, from graduate students to advanced users. Beginning with some foundational examples intended to build intuition for the theory to follow, including the theory of noncommutative decreasing arrangements, as developed by Fack and Kosaki, and of Orlicz spaces for general von Neumann algebras. The authors then present the theory of the more accessible tracial case, followed by that of the more demanding general (type III) case. The final part of the book is devoted to advanced theory and applications.
Geometry Lie Theory And Applications
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Author : Sigbjørn Hervik
language : en
Publisher: Springer Nature
Release Date : 2022-02-07
Geometry Lie Theory And Applications written by Sigbjørn Hervik and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.
This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
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.
Operator Theory By Example
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Author : Stephan Ramon Garcia
language : en
Publisher: Oxford University Press
Release Date : 2023
Operator Theory By Example written by Stephan Ramon Garcia 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 2023 with Mathematics categories.
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.
Categories For Quantum Theory
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Author : Chris Heunen
language : en
Publisher: Oxford University Press
Release Date : 2019-11-14
Categories For Quantum Theory written by Chris Heunen 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 2019-11-14 with Mathematics categories.
Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.