Presents quantum field theory from a unified global viewpoint, and clearly shows how classical field theory, quantum mechanics, and quantum field theory are related.
I: Classical Dynamical Theory; 1 Fundamentals; 2 Dynamics and Invariance Transformations; 3 Small Disturbances and Green’s Functions; 4 The Peierls Bracket; 5 Finite Disturbances. Tree Theorems. Asmptotic Fields; 6 Conservation Laws; II: The Heuristic Road to Quantization. The Quantum Formalism and its Interpretation; 7 Classical Theory of Measurement; 8 Quantum Theory of Measurement; 9 Interpretation of the Quantum Formalism I; 10 The Schwinger Variational Principle and the Feynman Functional Integral; 11 The Quantum Mechanics of Standard Canonical Systems; 12 Interpretation of the Quantum Formalism II; III: Evaluation and Approximation of Feynman Functional Integrals; 13 The Functional Integral for Standard Canonical Systems; 14 Approximation and Evaluation of the Path Integral; 15 The Nonrelativistic Particle in a Curved Space; 16 The Heat Kernel; IV: Linear Systems; 17 Linear Boson Fields in Stationary Backgrounds; 18 Quantization of Linear Boson Fields; 19 Linear Fermion Fields. Stationary Backgrounds; 20 Quantization of Linear Fermion Fields; 21 Linear Fields in Nonstationary Backgrounds; 22 Linear (or Linearized) Fields Possessing Invariant Flows; V: Nonlinear Fields; 23 The Effective Action, the S-matrix, and Slavnov-Taylor Identities; 24 Gauge Theories I. General Formalism; 25 Gauge Theories II. Background Field Methods. Scattering Theory; 26 Case-I Gauge Theory without Ghosts. Description of Cases II and III; VI: Tools for Quantum Field Theory. Applications; 27 The Heat Kernel; 28 Vacuum Currents. Anomalies; 29 More Vacuum Phenomena; 30 Black Hole Vacua. Hawking Radiation; 31 The Closed-time-path or In-in Formalism; VII: Special Topics; 32 Euclideanization and Renormalization; 33 Canonical Transformations. Space Inversion and Time Reversal; 34 Quantum Electrodynamics; 35 The Yang-Mills and Gravitational Fields; VIII: Examples. Simple Exercises in the use of the Global Formalism; X0 The Nonrelativistic Particle in Flat Space; X1 A Simple Fermi System; X2 A Fermi doublet; X3 Fermi Multiplet; X4 The Fermi Oscillator; X5 The Bose Oscillator; X6 A Fourth-order System; X7 A Model for Ghosts; X8 Free Scalar Field in Flat Spacetime; X9 Massive Vector Field in Four-dimensional Flat Spacetime; X10 Massive Antisymmetric Tensor Field; X11 Massive Symmetric Tensor Field in Flat Spacetime; X12 Massive Spinor Field in Flat Spacetime; X13 Massive spin-3/2 Field in Flat Spacetime; X14 Electromagnetic Field in Flat Spacetime; X15 Massless Symmetric Tensor Field in Flat Spacetime; X16 Massless Spinor Field in Four-dimensional Flat Spacetime; X17 Massless Spin-3/2 Field in Four-dimensional Flat Spacetime; X18 Renormalization Group and Spontaneous Symmetry Breaking in the (lambda phi) to the fourth power Model; X19 The Relativistic Particle in Minkowski Spacetime; X20 A Simple Soluble Nonlinear Model; X21 Quantum Mechanics on a Circle; X22 Quantum Mechanics on a Klein Bottle; X23 Ghosts for Ghosts; X24 Massless Antisymmetric Tensor Field