Quantum Field Theory of Many-Body Systems From the Origin of Sound to an Origin of Light and Electrons

ISBN-10: 019922725X
ISBN-13: 9780199227259
Edition: 2007
Authors: Xiao-Gang Wen
List price: $49.95
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Description: For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalization,  More...

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Book details

List price: $49.95
Copyright year: 2007
Publisher: Oxford University Press, Incorporated
Publication date: 10/18/2007
Binding: Paperback
Pages: 512
Size: 6.75" wide x 9.25" long x 1.00" tall
Weight: 1.892
Language: English

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalization, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics, which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, spin liquid and string condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at bringing students to the frontiers of research in condensed matter physics.

Introduction
More is different
'Elementary' particles and physics laws
Corner-stones of condensed matter physics
Topological order and quantum order
Origin of light and fermions
Novelty is more important than correctness
Remarks: evolution of the concept of elementary particles
Path integral formulation of quantum mechanics
Semiclassical picture and path integral
Linear responses and correlation functions
Quantum spin, the Berry phase, and the path integral
Applications of the path integral formulation
Interacting boson systems
Free boson systems and second quantization
Mean-field theory of a superfluid
Path integral approach to interacting boson systems
Superfluid phase at finite temperatures
Renormalization group
Boson superfluid to Mott insulator transition
Superfluidity and superconductivity
Perturbative calculation of the thermal potential
Free fermion systems
Many-fermion systems
Free fermion Green's function
Two-body correlation functions and linear responses
Quantized Hall conductance in insulators
Interacting fermion systems
Orthogonality catastrophe and X-ray spectrum
Hartree-Fock approximation
Landau Fermi liquid theory
Perturbation theory and the validity of Fermi liquid theory
Symmetry-breaking phase and the spin-density-wave state
Nonlinear [sigma]-model
Quantum gauge theories
Simple gauge theories
Z[subscript 2] lattice gauge theory
U(1) gauge theory and the XY-model in 1 + 2 dimensions
The quantum U(1) gauge theory on a lattice
Theory of quantum Hall states
The Aharonov-Bohm effect and fractional statistics
The quantum Hall effect
Effective theory of fractional quantum Hall liquids
Edge excitations in fractional quantum Hall liquids
Topological and quantum order
States of matter and the concept of order
Topological order in fractional quantum Hall states
Quantum orders
A new classification of orders
Mean-field theory of spin liquids and quantum order
Projective construction of quantum spin-liquid states
The SU(2) projective construction
Topological orders in gapped spin-liquid states
Quantum orders in symmetric spin liquids
Continuous phase transitions without symmetry breaking
The zoo of symmetric spin liquids
Physical measurements of quantum orders
The phase diagram of the J[subscript 1]-J[subscript 2] model in the large-N limit
Quantum order and the stability of mean-field spin liquids
Quantum order and gapless gauge bosons and fermions
String condensation-an unification of light and fermions
Local bosonic models
An exactly soluble model from a projective construction
Z[subscript 2] spin liquids and string-net condensation
Classification of string-net condensations
Emergent fermions and string-net condensation
The quantum rotor model and U(1) lattice gauge theory
Emergent light and electrons from an SU(N[subscript f]) spin model
Index

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