Preface Part. I Quantum Field Theory 1. Quantum Mechanics 1.1 Hilbert Spaces 1.2 Canonical Formalism 1.3 Creation and Annihilation Operators 1.4 Uncertainty Principle 1.5 Coherent States and von Neumann Lattice 1.6 Squeezed Coherent State 1.7 Particle Number and Phase 1.8 Macroscopic Coherence 2. Quantum Field Theory 2.1 One-Body Hamiltonian 2.2 Many-Body Hamiltonian 2.3 Boson Field Operators 2.4 Quantum Field Theory 2.5 Fermion Field Operators 2.6 Electrons Interacting with Electromagnetic Field 3. Canonical Quantization 3.1 Relativistic Particles and Waves 3.2 Schr6dinger Field 3.3 Real Klein-Gordon Field 3.4 Complex Klein-Gordon Field 3.5 Nother Currents 4. Spontaneous Symmetry Breaking 4.1 Ferromagnets 4.2 Real Klein-Gordon Field 4.3 Complex Klein-Gordon Field 4.4 Sigma Model 4.5 Spin Field 4.6 Schrodinger Field 4.7 Superfluidity 4.8 Goldstone Theorem 5. Electromagnetic Field 5.1 Maxwell Equations 5.2 Canonical Quantization 5.3 Interaction with Matter Field 5.4 Anderson-Higgs Mechanism 5.5 Massive Vector Field 5.6 Superconductivity 5.7 Aharonov-Bohm Effect 6. Dirac Field 6.1 Dirac Equation 6.2 Plane Wave Solutions 6.3 Canonical Quantization 6.4 Interaction with Electromagnetic Field 6.5 Weyl Field (Massless Dirac Field) 6.6 Massless Dirac Electrons in Magnetic Field 7. Topological Solitons 7.1 Topological Sectors
7.2 Classical Fields 7.3 Solitary Waves, Kinks and Solitons 7.4 Sine-Gordon Solitons 7.5 Vortex Solitons 7.6 Homotopy Classes 7.7 0(3) Skyrmions 7.8 SU(N) Skyrmions or CPN-1 Skyrmions 7.9 Skyrmions in Ferromagnets 8. Anyons 8.1 Spin and Statistics …… Part. II Monolayer Quantum Hall Systems 9. Overview of Monolayer QH Systems 10. Landau Quantization 11. Quantum Hall Effects 12. Quasiparticles and Activation Energy 13. Field Theory of Composite Particles 14. Composite Bosons and Semiclassical Analysis 15. Quantum Hall Ferromagnets 16. Spin Textures 17. Hierarchy of Fractional QH States 18. Edge Effects 19. Stripes and Bubbles in Higher Landau Levels 20. Quantum Hall Effects in Graphene 21. Quantum Hall Effects in Silicene 22. Topological Insulators and QH Effects without Landau Levels Part. III Bilayer Quantum Hall Systems 23. Overview of Bilayer QH Systems 24. SU(2) Pseudospin Structure 25. Bilayer-Locked States 26. Interlayer Coherence and Josephson Effects 27. Commensurate and Incommensurate Phases 28. SU(4) Quantum Hall Ferromagnets 29. Bilayer Quantum Hall Systems at v = 2 Part. IV Microscopic Theory 30. Overview of Microscopic Theory 31. Noncommutative Geometry 32. Landau Level Projection 33. Noncommutative Solitons 34. Exchange Interactions and Effective Theory Part. V Recent Experimental Developments 35. Overview of New Experimental Developments 36. Real-Space Observation of Quantum Hall States 37. Collective Excitations in Integer and Fractional QH Systems 38. Hyperfine Interactions in Quantum Hall Regime 39. Microwave-induced Nonequilibrium Phenomena 40. Superfluid Properties of Electron Bilayers 41. Quantum Hall Effect in ZnO Appendices References
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