Preface |
Bosons / 1: |
The simple harmonic oscillator / 1.1: |
Annihilation and creation operators / 1.2: |
Coupled oscillators: the linear chain / 1.3: |
Three-dimensional lattices and vector fields / 1.4: |
The continuum limit / 1.5: |
Classical field theory / 1.6: |
Second quantization / 1.7: |
Klein--Gordon equation / 1.8: |
Sources of a field, and interactions between fields / 1.9: |
Example: Rayleigh scattering of phonons / 1.10: |
Example: Yukawa force / 1.11: |
Charged bosons / 1.12: |
Fermions / 2: |
Occupation-number representation / 2.1: |
Annihilation and creation operators: anticommutation / 2.2: |
Scattering: connection with statistical mechanics / 2.3: |
Interactions between particles: momentum conservation / 2.5: |
Fermion--boson interaction / 2.6: |
Holes and antiparticles / 2.7: |
Perturbation theory / 3: |
The Brillouin--Wigner series / 3.1: |
The Heisenberg representation / 3.2: |
Interaction representation / 3.3: |
Time--integral expansion series / 3.4: |
S-matrix / 3.5: |
S-matrix expansion: algebraic theory / 3.6: |
Diagrammatic representation / 3.7: |
Momentum representation / 3.8: |
The physical vacuum / 3.9: |
Dyson's equation and renormalization / 3.10: |
Green functions / 4: |
The density matrix / 4.1: |
Equation of motion of density operator / 4.2: |
Ensembles in thermal equilibrium / 4.3: |
The Kubo formula / 4.4: |
The one-particle Green function / 4.5: |
Energy--momentum representation / 4.6: |
Evaluation of Green functions / 4.7: |
Two-particle Green functions / 4.8: |
The hierarchy of Green functions / 4.9: |
Time-independent Green functions / 4.10: |
Matrix representation of the Green function / 4.11: |
Space representation of time-independent Green function / 4.12: |
The Born series / 4.13: |
The T-matrix / 4.14: |
Example: impurity states in a metal / 4.15: |
Some aspects of the many-body problem / 5: |
Quantum properties of macroscopic systems / 5.1: |
Statistical methods: the Thomas--Fermi approximation / 5.2: |
Hartree self-consistent field / 5.3: |
The Hartree--Fock method / 5.4: |
Diagrammatic interpretation of Hartree--Fock theory / 5.5: |
The Brueckner method / 5.6: |
The dielectric response function / 5.7: |
Spectral representation of dielectric function / 5.8: |
Diagrammatic interpretation of dielectric screening / 5.9: |
The random phase approximation / 5.10: |
The Landau theory of Fermi liquids / 5.11: |
The dilute Bose gas / 5.12: |
The superconducting state / 5.13: |
Relativistic formulations / 6: |
Lorentz invariance / 6.1: |
Relativistic electromagnetic theory / 6.2: |
The wave equation and gauge invariance / 6.3: |
Quantization of relativistic fields / 6.4: |
Spinors / 6.5: |
The Dirac equation / 6.6: |
The Dirac matrices / 6.7: |
Quantization of the Dirac field / 6.8: |
Interactions between relativistic fields / 6.9: |
Relativistic kinematics / 6.10: |
The analytic S-matrix / 6.11: |
The algebra of symmetry / 7: |
Symmetry operations / 7.1: |
Representations / 7.2: |
Regular representations of finite groups / 7.3: |
The orthogonality theorem / 7.4: |
Character and class / 7.5: |
Product groups and representations / 7.6: |
Translation groups / 7.7: |
Continuous groups / 7.8: |
The rotation group / 7.9: |
Irreducible representations of the rotation group / 7.10: |
Spinor representations / 7.11: |
SU(2) / 7.12: |
SU(3) / 7.13: |
Index |
Preface |
Bosons / 1: |
The simple harmonic oscillator / 1.1: |