Topological and Algebraic Methods in Contemporary Mathematical Physics
Book
Hardback
160 pages
978-0-415-29919-0 (ISBN)
Description
This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three sections: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin; the second part presents algebraic geometry analysis of the Yang-Baxter equations for two dimensional models; part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementary and convenient for applications.
More details
Series
Language
English
Place of publication
London
United Kingdom
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 234 mm
Width: 156 mm
ISBN-13
978-0-415-29919-0 (9780415299190)
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Schweitzer Classification
Persons
Content
1.0 Introduction 1.1 Hamiltonian Formalism, Simplest Examples, Systems of Kirchhoff type 1.2 Hamiltonian Formalism for Systems of Hydrodynamic Origin 1.3 What is Morse Theory? 1.4 Equations of Kirchhoff type and the Dirac Monopole 1.5 Multivalued functionals and the analogue of the Morse Theory. The Periodic Problem for Equations of Kirchhoff type. Chiral Fields in an External Field 2.0 Introduction 2.1 Vacuum Vectors and Algebraic Curves 2.2 The Baxter Equations 2.3 Solutions of Rank 2 3.0 Introduction 3.1 Information from the Theory of Theta Functions and Riemann Surfaces 3.2 Clebsch-Gordon-Baxter-Akhiezer Functions. Integrations of Nonlinear Equations 3.3 Application of Nonlinear Equations to Classical Problems of the Theory of Riemann Surfaces and their Theta Functions