| Preface | p. v |
| Bosons | |
| The simple harmonic oscillator | p. 1 |
| Annihilation and creation operators | p. 3 |
| Coupled oscillators: the linear chain | p. 5 |
| Three-dimensional lattices and vector fields | p. 9 |
| The continuum limit | p. 12 |
| Classical field theory | p. 14 |
| Second quantization | p. 18 |
| Klein--Gordon equation | p. 21 |
| Sources of a field, and interactions between fields | p. 22 |
| Example: Rayleigh scattering of phonons | p. 24 |
| Example: Yukawa force | p. 26 |
| Charged bosons | p. 28 |
| Fermions | |
| Occupation-number representation | p. 32 |
| Annihilation and creation operators: anticommutation | p. 33 |
| Second quantization | p. 36 |
| Scattering: connection with statistical mechanics | p. 39 |
| Interactions between particles: momentum conservation | p. 41 |
| Fermion--boson interaction | p. 43 |
| Holes and antiparticles | p. 48 |
| Perturbation theory | |
| The Brillouin--Wigner series | p. 53 |
| The Heisenberg representation | p. 56 |
| Interaction representation | p. 60 |
| Time--integral expansion series | p. 62 |
| S-matrix | p. 64 |
| S-matrix expansion: algebraic theory | p. 67 |
| Diagrammatic representation | p. 74 |
| Momentum representation | p. 80 |
| The physical vacuum | p. 86 |
| Dyson's equation and renormalization | p. 90 |
| Green functions | |
| The density matrix | p. 94 |
| Equation of motion of density operator | p. 98 |
| Ensembles in thermal equilibrium | p. 99 |
| The Kubo formula | p. 101 |
| The one-particle Green function | p. 104 |
| Energy--momentum representation | p. 107 |
| Evaluation of Green functions | p. 110 |
| Two-particle Green functions | p. 112 |
| The hierarchy of Green functions | p. 116 |
| Time-independent Green functions | p. 117 |
| Matrix representation of the Green function | p. 120 |
| Space representation of time-independent Green function | p. 122 |
| The Born series | p. 124 |
| The T-matrix | p. 127 |
| Example: impurity states in a metal | p. 129 |
| Some aspects of the many-body problem | |
| Quantum properties of macroscopic systems | p. 135 |
| Statistical methods: the Thomas--Fermi approximation | p. 136 |
| Hartree self-consistent field | p. 138 |
| The Hartree--Fock method | p. 140 |
| Diagrammatic interpretation of Hartree--Fock theory | p. 143 |
| The Brueckner method | p. 146 |
| The dielectric response function | p. 148 |
| Spectral representation of dielectric function | p. 150 |
| Diagrammatic interpretation of dielectric screening | p. 154 |
| The random phase approximation | p. 158 |
| The Landau theory of Fermi liquids | p. 162 |
| The dilute Bose gas | p. 167 |
| The superconducting state | p. 170 |
| Relativistic formulations | |
| Lorentz invariance | p. 175 |
| Relativistic electromagnetic theory | p. 177 |
| The wave equation and gauge invariance | p. 180 |
| Quantization of relativistic fields | p. 183 |
| Spinors | p. 187 |
| The Dirac equation | p. 191 |
| The Dirac matrices | p. 193 |
| Quantization of the Dirac field | p. 196 |
| Interactions between relativistic fields | p. 199 |
| Relativistic kinematics | p. 203 |
| The analytic S-matrix | p. 207 |
| The algebra of symmetry | |
| Symmetry operations | p. 213 |
| Representations | p. 215 |
| Regular representations of finite groups | p. 219 |
| The orthogonality theorem | p. 222 |
| Character and class | p. 225 |
| Product groups and representations | p. 230 |
| Translation groups | p. 235 |
| Continuous groups | p. 237 |
| The rotation group | p. 241 |
| Irreducible representations of the rotation group | p. 244 |
| Spinor representations | p. 247 |
| SU(2) | p. 249 |
| SU(3) | p. 254 |
| Index | p. 259 |
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