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This is a textbook of advanced quantum theory for graduate students and research workers which gives a connected mathematical derivation of the important results, concentrating on the central ideas without burdening the exposition with elaborate detail or unnecessary rigour, and explains, in the simplest possible terms, the symbols and concepts which frequently confront the active research worker in solid state, nuclear and high-energy physics, and in theoretical chemistry. Professor Ziman brings to his task the sympathetic guidance of a lecturer who has not forgotten the difficulties that he himself had to surmount in mastering his subject.

Tabla de contenidos provista por Syndetics

• Preface(p. v)
• 1 Bosons
• 1.1 The simple harmonic oscillator(p. 1)
• 1.2 Annihilation and creation operators(p. 3)
• 1.3 Coupled oscillators: the linear chain(p. 5)
• 1.4 Three-dimensional lattices and vector fields(p. 9)
• 1.5 The continuum limit(p. 12)
• 1.6 Classical field theory(p. 14)
• 1.7 Second quantization(p. 18)
• 1.8 Klein--Gordon equation(p. 21)
• 1.9 Sources of a field, and interactions between fields(p. 22)
• 1.10 Example: Rayleigh scattering of phonons(p. 24)
• 1.11 Example: Yukawa force(p. 26)
• 1.12 Charged bosons(p. 28)
• 2 Fermions
• 2.1 Occupation-number representation(p. 32)
• 2.2 Annihilation and creation operators: anticommutation(p. 33)
• 2.3 Second quantization(p. 36)
• 2.4 Scattering: connection with statistical mechanics(p. 39)
• 2.5 Interactions between particles: momentum conservation(p. 41)
• 2.6 Fermion--boson interaction(p. 43)
• 2.7 Holes and antiparticles(p. 48)
• 3 Perturbation theory
• 3.1 The Brillouin--Wigner series(p. 53)
• 3.2 The Heisenberg representation(p. 56)
• 3.3 Interaction representation(p. 60)
• 3.4 Time--integral expansion series(p. 62)
• 3.5 S-matrix(p. 64)
• 3.6 S-matrix expansion: algebraic theory(p. 67)
• 3.7 Diagrammatic representation(p. 74)
• 3.8 Momentum representation(p. 80)
• 3.9 The physical vacuum(p. 86)
• 3.10 Dyson's equation and renormalization(p. 90)
• 4 Green functions
• 4.1 The density matrix(p. 94)
• 4.2 Equation of motion of density operator(p. 98)
• 4.3 Ensembles in thermal equilibrium(p. 99)
• 4.4 The Kubo formula(p. 101)
• 4.5 The one-particle Green function(p. 104)
• 4.6 Energy--momentum representation(p. 107)
• 4.7 Evaluation of Green functions(p. 110)
• 4.8 Two-particle Green functions(p. 112)
• 4.9 The hierarchy of Green functions(p. 116)
• 4.10 Time-independent Green functions(p. 117)
• 4.11 Matrix representation of the Green function(p. 120)
• 4.12 Space representation of time-independent Green function(p. 122)
• 4.13 The Born series(p. 124)
• 4.14 The T-matrix(p. 127)
• 4.15 Example: impurity states in a metal(p. 129)
• 5 Some aspects of the many-body problem
• 5.1 Quantum properties of macroscopic systems(p. 135)
• 5.2 Statistical methods: the Thomas--Fermi approximation(p. 136)
• 5.3 Hartree self-consistent field(p. 138)
• 5.4 The Hartree--Fock method(p. 140)
• 5.5 Diagrammatic interpretation of Hartree--Fock theory(p. 143)
• 5.6 The Brueckner method(p. 146)
• 5.7 The dielectric response function(p. 148)
• 5.8 Spectral representation of dielectric function(p. 150)
• 5.9 Diagrammatic interpretation of dielectric screening(p. 154)
• 5.10 The random phase approximation(p. 158)
• 5.11 The Landau theory of Fermi liquids(p. 162)
• 5.12 The dilute Bose gas(p. 167)
• 5.13 The superconducting state(p. 170)
• 6 Relativistic formulations
• 6.1 Lorentz invariance(p. 175)
• 6.2 Relativistic electromagnetic theory(p. 177)
• 6.3 The wave equation and gauge invariance(p. 180)
• 6.4 Quantization of relativistic fields(p. 183)
• 6.5 Spinors(p. 187)
• 6.6 The Dirac equation(p. 191)
• 6.7 The Dirac matrices(p. 193)
• 6.8 Quantization of the Dirac field(p. 196)
• 6.9 Interactions between relativistic fields(p. 199)
• 6.10 Relativistic kinematics(p. 203)
• 6.11 The analytic S-matrix(p. 207)
• 7 The algebra of symmetry
• 7.1 Symmetry operations(p. 213)
• 7.2 Representations(p. 215)
• 7.3 Regular representations of finite groups(p. 219)
• 7.4 The orthogonality theorem(p. 222)
• 7.5 Character and class(p. 225)
• 7.6 Product groups and representations(p. 230)
• 7.7 Translation groups(p. 235)
• 7.8 Continuous groups(p. 237)
• 7.9 The rotation group(p. 241)
• 7.10 Irreducible representations of the rotation group(p. 244)
• 7.11 Spinor representations(p. 247)
• 7.12 SU(2)(p. 249)
• 7.13 SU(3)(p. 254)
• Index(p. 259)