Book•
Many-Particle Physics
01 Jan 1981-
TL;DR: In this article, the authors present a model for the second quantization of a particle and show that it can be used to construct a pair distribution function with respect to a pair of spinless fermions.
Abstract: 1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.- C. Deformation Potential.- D. Piezoelectric Interaction.- E. Polar Coupling.- 1.4. Spin Hamiltonians.- A. Homogeneous Spin Systems.- B. Impurity Spin Models.- 1.5. Photons.- A. Gauges.- B. Lagrangian.- C. Hamiltonian.- 1.6. Pair Distribution Function.- Problems.- 2. Green's Functions at Zero Temperature.- 2.1. Interaction Representation.- A. Schrodinger.- B. Heisenberg.- C. Interaction.- 2.2. S Matrix.- 2.3. Green's Functions.- 2.4. Wick's Theorem.- 2.5. Feynman Diagrams.- 2.6. Vacuum Polarization Graphs.- 2.7. Dyson's Equation.- 2.8. Rules for Constructing Diagrams.- 2.9. Time-Loop S Matrix.- A. Six Green's Functions.- B. Dyson's Equation.- 2.10. Photon Green's Functions.- Problems.- 3. Green's Functions at Finite Temperatures.- 3.1. Introduction.- 3.2. Matsubara Green's Functions.- 3.3. Retarded and Advanced Green's Functions.- 3.4. Dyson's Equation.- 3.5. Frequency Summations.- 3.6. Linked Cluster Expansions.- A. Thermodynamic Potential.- B. Green's Functions.- 3.7. Real Time Green's Functions.- Wigner Distribution Function.- 3.8. Kubo Formula for Electrical Conductivity.- A. Transverse Fields, Zero Temperature.- B. Finite Temperatures.- C. Zero Frequency.- D. Photon Self-Energy.- 3.9. Other Kubo Formulas.- A. Pauli Paramagnetic Susceptibility.- B. Thermal Currents and Onsager Relations.- C. Correlation Functions.- Problems.- 4. Exactly Solvable Models.- 4.1. Potential Scattering.- A. Reaction Matrix.- B. T Matrix.- C. Friedel's Theorem.- D. Phase Shifts.- E. Impurity Scattering.- F. Ground State Energy.- 4.2. Localized State in the Continuum.- 4.3. Independent Boson Models.- A. Solution by Canonical Transformation.- B. Feynman Disentangling of Operators.- C. Einstein Model.- D. Optical Absorption and Emission.- E. Sudden Switching.- F. Linked Cluster Expansion.- 4.4. Tomonaga Model.- A. Tomonaga Model.- B. Spin Waves.- C. Luttinger Model.- D. Single-Particle Properties.- E. Interacting System of Spinless Fermions.- F. Electron Exchange.- 4.5. Polaritons.- A. Semiclassical Discussion.- B. Phonon-Photon Coupling.- C. Exciton-Photon Coupling.- Problems.- 5. Electron Gas.- 5.1. Exchange and Correlation.- A. Kinetic Energy.- B. Direct Coulomb.- C. Exchange.- D. Seitz' Theorem.- E. ?(2a).- F. ?(2b).- G. ?(2c).- H. High-Density Limit.- I. Pair Distribution Function.- 5.2. Wigner Lattice and Metallic Hydrogen.- Metallic Hydrogen.- 5.3. Cohesive Energy of Metals.- 5.4. Linear Screening.- 5.5. Model Dielectric Functions.- A. Thomas-Fermi.- B. Lindhard, or RPA.- C. Hubbard.- D. Singwi-Sjolander.- 5.6. Properties of the Electron Gas.- A. Pair Distribution Function.- B. Screening Charge.- C. Correlation Energies.- D. Compressibility.- 5.7. Sum Rules.- 5.8. One-Electron Properties.- A. Renormalization Constant ZF.- B. Effective Mass.- C. Pauli Paramagnetic Susceptibility.- D. Mean Free Path.- Problems.- 6. Electron-Phonon Interaction.- 6.1 Frohlich Hamiltonian.- A. Brillouin-Wigner Perturbation Theory.- B. Rayleigh-Schrodinger Perturbation Theory.- C. Strong Coupling Theory.- D. Linked Cluster Theory.- 6.2 Small Polaron Theory.- A. Large Polarons.- B. Small Polarons.- C. Diagonal Transitions.- D. Nondiagonal Transitions.- E. Dispersive Phonons.- F. Einstein Model.- G. Kubo Formula.- 6.3 Heavily Doped Semiconductors.- A. Screened Interaction.- B. Experimental Verifications.- C. Electron Self-Energies.- 6.4 Metals.- A. Phonons in Metals.- B. Electron Self-Energies.- Problems.- 7. dc Conductivities.- 7.1. Electron Scattering by Impurities.- A. Boltzmann Equation.- B. Kubo Formula: Approximate Solution.- C. Kubo Formula: Rigorous Solution.- D. Ward Identities.- 7.2. Mobility of Frohlich Polarons.- A. Single-Particle Properties.- B. ??1 Term in the Mobility.- 7.3. Electron-Phonon Interactions in Metals.- A. Force-Force Correlation Function.- B. Kubo Formula.- C. Mass Enhancement.- D. Thermoelectric Power.- 7.4. Quantum Boltzmann Equation.- A. Derivation of the Quantum Boltzmann Equation.- B. Gradient Expansion.- C. Electron Scattering by Impurities.- D. T2 Contribution to the Electrical Resistivity.- Problems.- 8. Optical Properties of Solids.- 8.1. Nearly Free-Electron System.- A. General Properties.- B. Force-Force Correlation Functions.- C. Frohlich Polarons.- D. Interband Transitions.- E. Phonons.- 8.2. Wannier Excitons.- A. The Model.- B. Solution by Green's Functions.- C. Core-Level Spectra.- 8.3. X-Ray Spectra in Metals.- A. Physical Model.- B. Edge Singularities.- C. Orthogonality Catastrophe.- D. MND Theory.- E. XPS Spectra.- Problems.- 9. Superconductivity.- 9.1. Cooper Instability.- 9.2. BCS Theory.- 9.3. Electron Tunneling.- A. Tunneling Hamiltonian.- B. Normal Metals.- C. Normal-Superconductor.- D. Two Superconductors.- E. Josephson Tunneling.- 9.4. Infrared Absorption.- 9.5. Acoustic Attenuation.- 9.6. Excitons in Superconductors.- 9.7. Strong Coupling Theory.- Problems.- 10. Liquid Helium.- 10.1. Pairing Theory.- A. Hartree and Exchange.- B. Bogoliubov Theory of 4He.- 10.2. 4He: Ground State Properties.- A. Off-Diagonal Long-Range Order.- B. Correlated Basis Functions.- C. Experiments on nk.- 10.3. 4He: Excitation Spectrum.- A. Bijl-Feynman Theory.- B. Improved Excitation Spectra.- C. Superfluidity.- 10.4. 3He: Normal Liquid.- A. Fermi Liquid Theory.- B. Experiments and Microscopic Theories.- C. Interaction between Quasiparticles: Excitations.- D. Quasiparticle Transport.- 10.5. Superfluid 3He.- A. Triplet Pairing.- B. Equal Spin Pairing.- Problems.- 11. Spin Fluctuations.- 11.1. Kondo Model.- A. High-Temperature Scattering.- B. Low-Temperature State.- C. Kondo Temperature.- 11.2. Anderson Model.- A. Collective States.- B. Green's Functions.- C. Spectroscopies.- Problems.- References.- Author Index.
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Cites background from "Many-Particle Physics"
...(60) More complicated operators can be written in terms of Green functions using Wick's theorem (Mahan, 1981, p. 95) which states that a a a a " a a a a ! a a a a ....
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...1 ImG (k, ) , (68) where the retarded Green function G (k, ) is given by (see Mahan, 1981, p. 135) G (k, )" dt e G (k, t) (69) and G (k, t)"!i (t) [a (t)a (0)#a (0)a (t)] "!i (t) (G #G ) ....
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Université catholique de Louvain1, Centre national de la recherche scientifique2, Université de Montréal3, French Alternative Energies and Atomic Energy Commission4, École normale supérieure de Lyon5, European Synchrotron Radiation Facility6, University of Liège7, University of Basel8, Université de Namur9, University of Milan10, Spanish National Research Council11, Dalhousie University12
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