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1.The Many-Body Problem in Classical Statistical Mechanics 1

1.1.The Ursell-Mayer Cluster Expansion 1

1.2.Correlation Functions 16

1.3.Cluster Expansion for Long-Range Forces 20

1.4.Plasma Oscillations;Random Phase Approximation 28

1.5.The Self-Consistent Field Method;Vlasov Equation 34

2.Field Theoretic Methods;Linked Cluster Expansion 40

2.1.Second Quantization;the Adiabatic Hypothesis 40

2.2.Perturbation Expansions 47

2.3.Linked Cluster Theorem 67

2.4.Grand Ensemble;Perturbation Theory 77

2.5.Canonical Ensemble;Perturbation Expansion 87

3.Electron Correlation;Quantum Mechanical Treatment 92

3.1.General Survey 92

3.2.The Sawada Hamiltonian Method 107

4.Dielectric Formulation of the Many-Body Problem 127

4.1.Generalized Dielectric Constant 127

4.2.Self-Consistent Field Method 138

4.3.Graphical Analysis of the Dielectric Constant 143

4.4.Corrections to RPA;Exchange Effects 148

4.5.RPA in Real Solids 151

5.Applications to the Theory of Metals 160

5.1.Specific Heat,Susceptibility,and Quasi-Particles 160

5.2.Characteristic Energy Loss 173

5.3.Screening of a Foreign Impurity 176

5.4.Phonons in Metals 179

5.5.Phonon-Mediated Electron Interaction—Mechanism of Superconductivity 189

5.6.Zero Sound 191

5.7.paramagnetic Spin Susceptibility 193

5.8.Other Applications of RPA 198

Author Index 201

Subject Index 203