Bethe Ansatz (Cambridge Monographs on Mathematical Physics)

Arutyunov, Gleb

Cambridge University Press（2026/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 608 p.
• 言語 ENG
• 商品コード 9781009664813
• DDC分類 530.15

Full Description

The Bethe Ansatz is a powerful method in the theory of quantum integrable models, essential for determining the energy spectrum of dynamical systems - from spin chains in magnetism to models in high-energy physics. This book provides a comprehensive introduction to the Bethe ansatz, from its historical roots to modern developments. First introduced by Hans Bethe in 1931, the method has evolved into a universal framework encompassing algebraic, analytic, thermodynamic, and functional forms. The book explores various Bethe ansatz techniques and their interrelations, covering both coordinate and algebraic versions, with particular attention to nested structures and functional relations involving transfer matrices. Advanced tools such as the separation of variables method are presented in detail. With a wealth of worked examples and precise calculations, this volume serves as an accessible and rigorous reference for graduate students and researchers in mathematical physics and integrable systems.

Contents

Preface; 1. Classical integrable systems; 2. Bethe wave function and S-matrix; 3. Coordinate Bethe Ansatz; 4. Transfer matrix method; 5. Nested coordinate Bethe Ansatz; 6. Algebraic approach to factorized scattering; 7. Algebraic Bethe Ansatz; 8. Functional methods; 9. Separation of variables.