Quantum field theory in condensed matter physics

Alexei M. Tsvelik

374 pages, parution le 14/11/2003 (2^eme édition)

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Résumé

This book is a course in modern quantum field theory as seen through the eyes of a theorist working in condensed matter physics. It contains a gentle introduction to the subject and therefore can be used even by graduate students. The introductory parts include a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals including a discussion of Landau-Fermi liquid theory. In later chapters the discussion gradually turns to more advanced methods used in the theory of strongly correlated systems.

The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.

Introduction to Methods
- QFT: language and goals
- Connection between quantum and classical: path integrals
- Definitions of correlation functions: Wick's theorem
- Free bosonic field in an external field
- Perturbation theory: Feynman diagrams
- Calculation methods for diagram series: divergences and their elimination
- Renormalization group procedures
- O(N)-symmetric vector model below the transition point
- Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion
- O(3)-nonlinear sigma model in the strong coupling limit
Fermions
- Path integral and Wick's theorem for fermions
- Interaction electrons: the concept of a Fermi liquid
- Electrodynamics in metals
- Relativistic fermions: aspects of quantum electrodynamics
- Aharonov-Bohm effect and transmutation of statistics
Strongly Fluctuating Spin Systems
- Schwinger-Wigner quantization procedure: nonlinear sigma models
- O(3)-nonlinear sigma model in (2+1) dimensions: the phase diagram
- Order from disorder
- Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3
- Majorana representations for spin S=1/2 magnets: relationship to Z2 lattice gauge theories
- Path integral representations for a doped antiferromagnet
Physics in the World of One Spatial Dimension
- Model of the free bosonic massless scalar field
- Relevant and irrelevant fields
- Kosterlitz-Thouless transition
- Conformal symmetry
- Virasoro algebra
- Differential equations for the correlation functions
- Ising model
- One-dimensional spinless fermions: Tomonaga-Luttinger liquid
- One-dimensional fermions with spin: spin-charge separation
- Kac-Moody algebras: Wess-Zumino-Novikov-Witten model
- Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization
- Semiclassical approach to WZNW models
- Integrable models: dynamical mass generation
- A comparative study of dynamical mass generation in one and three dimensions
- One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain
- Kondo chain
- Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics
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Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Alexei M. Tsvelik
Parution	14/11/2003
Édition	2^eme édition
Nb. de pages	374
Format	17,5 x 25,5
Couverture	Relié
Poids	910g
Intérieur	Noir et Blanc
EAN13	9780521822848