| Preface |
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xi | |
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xiii | |
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1 Introduction to Second Quantization |
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1 | (33) |
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1.1 Creation and Annihilation Operators |
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3 | (6) |
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1.2 Second Quantization for Bosons and Fermions |
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9 | (3) |
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12 | (4) |
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1.4 Model Hamiltonians for Interacting Boson or Fermion Particles |
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16 | (6) |
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1.5 Hamiltonian Diagonalization Methods |
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22 | (12) |
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31 | (3) |
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2 Time Evolution and Equations of Motion |
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34 | (33) |
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2.1 Operator Methods in Different Quantum Pictures |
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35 | (6) |
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2.2 Forced Quantum Harmonic Oscillator |
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41 | (3) |
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2.3 Time Evolution of Coherent States |
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44 | (2) |
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2.4 Lattice Dynamics for Phonons |
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46 | (5) |
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2.5 The Interacting Boson Gas Revisited |
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51 | (1) |
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2.6 Exchange and Dipole-Exchange Spin Waves |
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52 | (2) |
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2.7 Electronic Bands of Graphene |
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54 | (3) |
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2.8 Density Fluctuations in an Electron Gas |
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57 | (6) |
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63 | (4) |
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3 Formal Properties of Green's Functions |
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67 | (27) |
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3.1 Real-Time Green's Functions |
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68 | (4) |
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3.2 Time Correlation Functions |
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72 | (2) |
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3.3 Spectral Representations |
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74 | (3) |
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3.4 Real and Imaginary Parts of Green's Functions |
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77 | (5) |
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3.5 Imaginary-Time Green's Functions |
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82 | (6) |
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3.6 Methods of Evaluating Green's Functions |
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88 | (3) |
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91 | (3) |
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4 Exact Methods for Green's Function |
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94 | (21) |
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4.1 Noninteracting Gas of Bosons or Fermions |
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94 | (6) |
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4.2 Green's Functions for a Graphene Sheet |
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100 | (1) |
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4.3 Interaction of Light with Atoms |
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101 | (5) |
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4.4 Dipole-Exchange Ferromagnet |
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106 | (2) |
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4.5 Paramagnet with Crystal-Field Anisotropy |
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108 | (4) |
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112 | (3) |
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5 Green's Functions Using Decoupling Methods |
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115 | (33) |
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5.1 Hartree--Fock Theory for an Interacting Fermion Gas |
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115 | (5) |
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5.2 Random Phase Approximation for Ferromagnets |
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120 | (6) |
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5.3 Random Phase Approximation for Antiferromagnets |
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126 | (4) |
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5.4 Electron Correlations and the Hubbard Model |
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130 | (5) |
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5.5 The Anderson Model for Localized States in Metals |
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135 | (6) |
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5.6 Microscopic Theory of Superconductivity |
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141 | (5) |
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146 | (2) |
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6 Linear Response Theory and Green's Functions |
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148 | (28) |
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149 | (2) |
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6.2 Linear Response Theory |
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151 | (2) |
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6.3 Response Functions and Green's Functions |
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153 | (3) |
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6.4 Response Functions and Applications |
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156 | (4) |
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6.5 Phonons in an Infinite Elastic Medium |
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160 | (3) |
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6.6 Application to the Kubo Formalism |
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163 | (6) |
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6.7 Inelastic Light Scattering |
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169 | (4) |
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173 | (3) |
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7 Green's Functions for Localized Excitations |
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176 | (26) |
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7.1 Acoustic Phonons at Surfaces |
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176 | (3) |
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7.2 Surface Spin Waves in Ferromagnets |
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179 | (5) |
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7.3 Edge Modes in Graphene Nanoribbons |
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184 | (6) |
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7.4 Photonic Bands in Multilayer Superlattices |
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190 | (5) |
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7.5 Impurity Modes in Ferromagnets |
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195 | (4) |
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199 | (3) |
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8 Diagrammatic Perturbation Methods |
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202 | (31) |
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8.1 The Grand Partition Function |
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203 | (3) |
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206 | (6) |
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8.3 The Unperturbed Imaginary-Time Green's Function |
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212 | (1) |
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8.4 Diagrammatic Representation |
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213 | (11) |
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8.5 The Interacting Imaginary-Time Green's Function |
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224 | (6) |
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230 | (3) |
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9 Applications of Diagrammatic Methods |
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233 | (32) |
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9.1 Hartree--Fock Theory for Fermions |
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233 | (4) |
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9.2 Density Fluctuations in an Electron Gas |
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237 | (2) |
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9.3 Electron--Phonon Interactions |
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239 | (5) |
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9.4 Boson Expansion Methods for Spin Waves |
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244 | (3) |
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9.5 Scattering by Static Impurities |
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247 | (9) |
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9.6 Diagrammatic Techniques for Spin Operators |
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256 | (7) |
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263 | (2) |
| References |
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265 | (6) |
| Index |
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271 | |
Lisainfo e-raamatute kohta