Introduction to Green's Function Methods in Many-Body Physics : With Applications to Quantum Transport

Kantorovich, Lev

Cambridge University Press（2026/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 800 p.
• 言語 ENG
• 商品コード 9781009790147

Full Description

This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics. It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit. The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara function methods. The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches. Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters. The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers. More than 200 problems have been included to support learning, with selected solutions available at the end of each chapter. Instructors benefit from access to the full solutions manual.

Contents

List of Abbreviations; Part I. Preliminaries: 1. Second quantisation ignoring spin; 2. Second quantisation via relativistic treatment of many electrons; 3. Operators, interactions, Hamiltonians, mean field and linear response; Part II. Equilibrium: 4. Single-particle two-time Green's functions; 5. Matsubara (imaginary time) Green's functions; 6. Feynman diagrams for Matsubara Green's Functions; Part III. Non-Equilibrium: 7. Green's functions for non-equilibrium: definition and main properties; 8. Feynman diagrams for NEGF: perturbation theory; 9. Feynman diagrams for NEGF: variational approach; Part IV. Quantum Transport Applications: 10. Quantum transport in molecular junctions: steady state; 11. Quantum transport in molecular junctions: time-dependent bias; 12. Localised spins and transport: Kondo problem; A. Non-Hermitian Hamiltonian; B. Angular momentum of an electron; C. Canonical transformation; D. The delta function; References; Index.