Quantum field theory in condensed matter physics - Tsvelik, Alexei M. (Cambridge University Press, 2003)
Includes bibliographical references (page 358) and index
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
This book is a course in modern quantum field theory for condensed matter physics. The book is intended for graduate students, postdoctoral associates and independent researchers working condensed matter physics