Solitons, Instantons, and Twistors - Maciej Dunajski

. .

Auteur(s) : Maciej Dunajski

Editeur : Oxford University Press

Langue : Anglais

Parution : 01/05/2024

Format : Moyen, de 350g à 1kg

Nombre de pages : 416

Dimensions : 23.2 x 15.5 x 2.2

ISBN : 0198872542

Résumé :

• 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

...

Biographie:
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).


...

Sommaire:
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....