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