Quantum Field Theory in Condensed Matter Physics

by Alexei M. Tsvelik

Overview

This course in modern quantum field theory for condensed matter physics includes a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals. Alexei Tsvelik also covers Landau Fermi liquid theory and 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. First edition Hb (1995): 0-521-45467-0 First edition Pb (1996): 0-521-58989-4

Product Details

ISBN-13:	9780521529808
Publisher:	Cambridge University Press
Publication date:	01/18/2007
Edition description:	REV
Pages:	380
Product dimensions:	6.69(w) x 9.61(h) x 0.79(d)

Table of Contents

Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34. Integrable models: dynamical mass generation; 35. A comparative study of dynamical mass generation in one and three dimensions; 36. One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain; 37. Kondo chain; 38. Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics; Select bibliography; Index.

Editorial Reviews

"...the book will, as intended, find its greatest value in bridging the gap between courses based on one or another of the standard texts and the current research literature on low dimensional electron and spin model systems. The author's breezy writing style brightens the text." Physics Today

From the Publisher

For graduate students and researchers already familiar with the basics of quantum field theory, introduces the developments over the past few years in its application to problems in condensed matter physics. To jog memories, briefly reviews the essential methods including path integrals, Feynman diagrams, and renormalization. Then applies them to such topics as electrodynamics in metals, relativistic fermions, and the Aharonov-Bohm effect. Also discusses non-perturbative techniques, strongly fluctuating spin systems, conformal symmetry, Kondo chains, and related problems. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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