Solitons, Instantons, and Twistors

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Maciej Dunajski (Professor of Mathematical Physics, Professor of Mathematical Physics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge)

Solitons, Instantons, and Twistors

Maciej Dunajski (Professor of Mathematical Physics, Professor of Mathematical Physics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge)

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English

Oxford University Press
08 July 2024

Differential calculus & equations; Analytic geometry; Non-linear science

Series: Oxford Graduate Texts in Mathematics

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, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.

By: Maciej Dunajski (Professor of Mathematical Physics Professor of Mathematical Physics Department of Applied Mathematics and Theoretical Physics University of Cambridge)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 234mm, Width: 155mm, Spine: 20mm
Weight: 690g
ISBN: 9780198872542
ISBN 10: 0198872542
Series: Oxford Graduate Texts in Mathematics
Pages: 416
Publication Date: 08 July 2024
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

1: Integrability in classical mechanics 2: Soliton equations and the inverse scattering transform 3: Hamiltonian formalism and zero-curvature representation 4: Lie symmetries and reductions 5: Lagrangian formalism and field theory 6: Gauge field theory 7: Integrability of ASDYM and twistor theory 8: Symmetry reductions and the integrable chiral model 9: Vortices 10: Gravitational instantons 11: Anti-self-dual conformal structures

Maciej Dunajski is a Fellow of Clare College, and a Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics, at the University of Cambridge. His research interests are in differential and projective Geometry, Solitons, and General Theory of Relativity. In 2021 he was awarded the Atiyah Fellowship by the London Mathematical Society. Dunajski is the winner of the 2023 Gravity Research Foundation Award, and the author of Geometry: A Very Short Introduction (OUP 2022).

Reviews for Solitons, Instantons, and Twistors

The great strength of this volume is how self-contained it is in its approach, one seldom needs to look elsewhere before delving headfirst into this volume. In my own work, this text is often my first go-to choice whenever I require reference.A particular strength of the text is its firm modern introduction to integrability, as well as its gentle and instructive introduction to gravitational instantons and twistor theory. This text is suitable for a graduate-level reader base whose education has at least included a first course in quantum field theory and general relativity. * Kymani Armstrong-Williams, Physics Book Reviews *