## Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and ElectronsFor 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 fractionalisation, 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 fermions in the universe. This book is apedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipativequantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are 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-bosontheory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics. |

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### Contents

1 Introduction | 1 |

2 Path integral formulation of quantum mechanics | 14 |

3 Interacting boson systems | 68 |

4 Free fermion systems | 144 |

5 Interacting fermion systems | 187 |

6 Quantum gauge theories | 250 |

### Other editions - View all

Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an ... Xiao-Gang Wen No preview available - 2007 |

Quantum Field Theory of Many-Body Systems:From the Origin of Sound to an ... Xiao-Gang Wen No preview available - 2004 |

### Common terms and phrases

algebraic ansatz assume Berry phase boson system bosonic model calculate characterized charge chiral spin correlation functions correspond density described dimensions discussion edge excitations eigenstates electron equation of motion Fermi liquid theory Fermi surface flux FQH liquids free fermion system gapless excitations gauge bosons gauge field gauge fluctuations gauge structure gauge transformation given Hamiltonian Hilbert space hopping instanton interaction invariant label Lagrangian Landau Laughlin light and fermions linear long-range order loop low-energy effective theory many-body massless mean-field theory momentum obtain operator order parameter particle path integral perturbation phase transition phonons physical spin potential Problem propagator properties quantized quantum orders quasihole quasiparticle result Section spectrum spin wave spinons string string-net condensation superfluid symmetry group symmetry-breaking T-flux temperature term time-ordered topological orders tunneling two-dimensional vector vortex wave function XY-model zero