Part Ⅰ.Nonrelativistic Many-Particle Systems
1.Second Quantization
1.1 Identical Particles, Many-Particle States, and Permutation Symmetry
1.1.1 States and Observables of Identical Particles
1.1.2 Examples
1.2 Completely Symmetric and Antisymmetric States
1.3 Bosons
1.3.1 States, Fock Space, Creation and Annihilation Operators
1.3.2 The Particle-Number Operator
1.3.3 General Single- and Many-Particle Operators
1.4 Fermions
1.4.1 States, Fock Space, Creation and Annihilation Operators
1.4.2 Single-and Many-Particle Operators
1.5 Field Operators
1.5.1 Transformations Between Different Basis Sy8tems
1.5.2 Field Operators
1.5.3 Field Equations
1.6 Momentum Representation
1.6.1 Momentum Eigen functions and the Hamiltonian
1.6.2 Fourier Transformation of the Density
1.6.3 The Inclusion of Spin
Problems
2.Spin-1/2 Fermions
2.1 Noninteracting Fermions
2.1.1 The Fermi Sphere, Excitations
2.1.2 Single-Particle Correlation Function
2.1.3 Pair Distribution Function
2.1.4 Pair Distribution Function, Density Correlation Functions, and Structure Factor
2.2 Ground State Energy and Elementary Theory of the Electron Gas
2.2.1 Hamiltonian
2.2.2 Ground State Energy in the Hartree-Fock Approximation
2.2.3 Modification of Electron Energy Levels due to the Coulomb Interaction
2.3 Hartree-Fock Equations for Atoms
Problems
3.Bosons
3.1 Free Bosons
3.1.1 Pair Distribution Function for Free Bosons
3.1.2 Two-Particle States of Bosons
3.2 Weakly Interacting, Dilute Bose Gas
3.2.1 Quantum Fluids and Bose-Einstein Condensation
3.2.2 Bogoliubov Theory of the Weakly Interacting Bose Gas
3.2.3 Superfluidity
Problems
4.Correlation Functions, Scattering, and Response
4.1 Scattering and Response
4.2 Density Matrix, Correlation Functions
4.3 Dynamical Susceptibility
4.4 Dispersion Relations
4.5 Spectral Representation
4.6 Fluctuation-Dissipation Theorem
4.7 Examples of Applications
4.8 Symmetry Properties
4.8.1 General Symmetry Relations
4.8.2 Symmetry Properties of the Response Function for Hermitian Operators
4.9 Sum Rules
4.9.1 General Structure of Sum Rules
4.9.2 Application to the Excitations in He Ⅱ
Problems
Bibliography for Part Ⅰ
Part Ⅱ.Relativistic Wave Equations
Part Ⅲ.Relativi8tic Fields
Appendix
Index