Quantum Hall Effects

Text:

Z.F.Ezawa, "Quantum Hall Effects: Field Theoretical Approach & Related Topics", World Scientific, 2nd ed., 2008.

Mathematical Supplement

Part 1. Quantum Field Theory


Chapter 1: Quantum Mechanics

  •    1.5. Coherent States & Von Neumann Lattice       ( Dec 22, 2014 )
  •    1.6. Squeezed Coherent State       ( Oct 22, 2014 )
  •    1.7. Particle Number & Phase       ( Oct 08, 2014 )
  •    1.8. Macroscopic Coherence       ( Oct 08, 2014 )
  •    Chap.1.zip       ( Dec 22, 2014 )

    Chapter 3: Canonical Quantization

  •    Plane Waves & Fourier Transforms       ( Oct 10, 2014 )
  •    3.2. Schrodinger Field       ( Oct 10, 2014 )
  •    3.3. Real Klein-Gordon Scalar Field       ( Oct 12, 2014 )
  •    3.4. Complex Klein-Gordon Field       ( Oct 12, 2014 )
  •    3.5. Noether Currents       ( Oct 13, 2014 )
  •    Chap.3.zip       ( Nov 27, 2014 )

    Chapter 4: Spontaneous Symmetry Breaking

  •    4.1. Ferromagnets       ( Oct 14, 2014 )
  •    4.2. Real Klein-Gordon Field       ( Oct 16, 2014 )
  •    4.3. Complex Klein-Gordon Field       ( Oct 16, 2014 )
  •    4.4. Sigma Model       ( Oct 17, 2014 )
  •    4.5. Schrodinger Field       ( Oct 22, 2014 )
  •    4.6. Superfluidity       ( Oct 23, 2014 )
  •    4.7. Goldstone Theorem       ( Oct 23, 2014 )
  •    Chap.4.zip       ( Nov 27, 2014 )

    Chapter 5: Electromagnetic Fields

  •    5.1. Maxwell Equations       ( Oct 27, 2014 )
  •    5.2. Canonical Quantization
  •       a)    Vacuum, Coulomb Gauge       ( Oct 29, 2014 )
  •       b)    Vacuum, Lorentz Gauge       ( Oct 29, 2014 )
  •       c)    Linear medium, Coulomb Gauge       ( Oct 30, 2014 )
  •       d)   Spin of Photons       ( Oct 30, 2014 )
  •    5.3. Interaction with Matter Field       ( Oct 31, 2014 )
  •    5.4. Anderson-Higgs Mechanism       ( Nov 23, 2014 )
  •    5.5. Massive Vector Field       ( Nov 01, 2014 )
  •    5.6. Superconductivity
  •       a)   Spontaneous Broken Symmetry for Cooper Pairs       ( Nov 02, 2014 )
  •       b)   Supercurrent       ( Nov 03, 2014 )
  •       c)   Meissner Effect       ( Nov 03, 2014 )
  •       d)   Flux Quantization       ( Nov 04, 2014 )
  •       e)   Vortices       ( Nov 04, 2014 )
  •       f)   Energy of a Vortex       ( Nov 04, 2014 )
  •       g)   Interaction between Vortices       ( Nov 05, 2014 )
  •    5.7. Aharonov-Bohm Effect
  •       a)   Fields of a Long Solenoid       ( Nov 05, 2014 )
  •       b)   Gauge Invariant Matter Field       ( Nov 05, 2014 )
  •       c)   Interference Experiment       ( Nov 06, 2014 )
  •       d)   Simple Dynamic Model       ( Nov 06, 2014 )
  •    Chap.5.zip       ( Nov 27, 2014 )

    Chapter 6: Dirac Field

  •    6.1. Dirac Equation       ( Nov 14, 2014 )
  •    6.2. Plane Wave Solutions       ( Nov 11, 2014 )
  •    6.3. Canonical Quantization       ( Nov 12, 2014 )
  •       a)   Fermi Sea       ( Nov 18, 2014 )
  •    6.4. Interaction with EM Fields       ( Nov 13, 2014 )
  •       a)   Nonrelativistic Limit       ( Nov 14, 2014 )
  •    6.5. Weyl Field       ( Nov 15, 2014 )
  •    6.6. Dirac Electrons in Magnetic Field       ( Nov 17, 2014 )
  •       a)   SUSY Quantum Mechanics       ( Nov 18, 2014 )
  •    Chap.6.zip       ( Nov 27, 2014 )

    Chapter 7: Topological Solitons

  •    7.1. Topological Sectors       ( Nov 19, 2014 )
  •    7.2. Classical Fields       ( Nov 19, 2014 )
  •    7.3. Solitary Waves, Kinks & Solitons       ( Nov 20, 2014 )
  •    7.4. Sine-Gordon Solitons       ( Nov 22, 2014 )
  •           SGkinks.nb
  •    7.5. Vortex Solitons
  •       a)   Flux Quantization       ( Nov 24, 2014 )
  •       b)   Small Fluctuations       ( Nov 24, 2014 )
  •    7.6. Homotopy Classes
  •       a)   Homotopy Group       ( Nov 25, 2014 )
  •       b)   Application to Vortex       ( Nov 25, 2014 )
  •       c)   Skyrmions       ( Nov 25, 2014 )
  •       d)   Scaling Theorem       ( Dec 02, 2014 )
  •    7.7. O(3) Skyrmions
  •       a)   Topological Charge       ( Nov 26, 2014 )
  •       b)   General Solution for Skyrmions       ( Nov 27, 2014 )
  •       c)   Examples       ( Nov 27, 2014 )
  •       d)   Solutions in Polar Form       ( Dec 02, 2014 )
  •       e)   Examples Revisited       ( Dec 02, 2014 )
  •       f)   Physical Models       ( Nov 27, 2014 )
  •    7.8. CPN-1 Skyrmions
  •       a)   Preliminaries       ( Nov 30, 2014 )
  •       b)   CPN-1 Sigma Model       ( Dec 01, 2014 )
  •       c)   Projective Representative       ( Nov 30, 2014 )
  •       d)   Topological Charge       ( Dec 01, 2014 )
  •       e)   Skyrmion Solutions       ( Dec 01, 2014 )
  •       f)   Topological Charge Density       ( Dec 01, 2014 )
  •       g)   Example       ( Dec 01, 2014 )
  •       h)   O(3) & CP1 Sigma Models       ( Dec 01, 2014 )
  •    Chap.7.zip       ( Dec 02, 2014 )

    Chapter 8: Anyons

  •    8.1. Spin & Statistics       ( Dec 04, 2014 )
  •    8.3. Quantum Mechanics       ( Dec 09, 2014 )
  •       a)   System of 2 Anyons       ( Dec 08, 2014 )
  •    8.4. Chern-Simons Gauge Theory       ( Dec 09, 2014 )
  •       a)   Equivalence to QM System       ( Dec 11, 2014 )
  •    8.5. Anyon Field Operators       ( Dec 12, 2014 )
  •    Chap.8.zip       ( Dec 12, 2014 )

    Appendices

  •    D. Groups SU(N) & SU(2N)       ( Dec 02, 2014 )
  •    I. Exchange Interaction       ( May 11, 2014 )
  •    L. 1-D Soliton Solutions       ( Nov 21, 2014 )

  •      

    Zip file for Part 1 :     Part.1.zip


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