A First Book of Quantum Field Theory

For more than 50 years we have known that quantum field theory is necessary for describing precision experiments involving electromagnetic interactions. More recently it has become clear that it also describes weak and strong interactions, and, in fact, produces an appropriate framework for describing a wide class of phenomena in the energy range covered by all experiments to date. A First Book of Quantum Field Theory introduces the subject as an elegant yet relatively simple piece of machinery with a broad range of applications. Although many introductory textbooks approach the subject with description of the electron and the photon as their goal, this treatment takes a rather unique approach through decay processes, which are, in some ways, simpler than scattering processes. Using decay processes allows the authors to introduce the basic machinery of Feynman diagrams even before addressing the quantization of spin-1 fields. With clear, engaging prose, strategically placed exercises, and canonical quantization employed throughout the book, A First Book of Quantum Field Theory offers a systematic, straightforward treatment ideal for advanced undergraduate and beginning post-graduate students. Readers will not only grasp the crucial concepts and the tools fundamental to the subject, but they will also discover both its elegance and its utility.

Table of Contents:
PRELIMINARIES Why Quantum Field Theory Creation and Annihilation Operators Special Relativity Space and Time in Relativistic Quantum Theory Natural Units CLASSICAL FIELD THEORY A quick review of particle mechanics Euler-Lagrange Equations in Field Theory Hamiltonian Formalism Noether's Theorem QUANTIZATION OF SCALAR FIELDS Equation of Motion The Field and its Canonical Quantization Fourier Decomposition of the Field Ground State of the Hamiltonian and Normal Ordering Fock Space Complex Scalar Field Propagator QUANTIZATION OF DIRAC FIELDS Dirac Hamiltonian Dirac Equation Plane Wave Solutions of Dirac Equation Projection Operators Lagrangian for a Dirac Field FourIer Decomposition of the Field Propagator THE S-MATRIX EXPANSION Examples of Interactions Evolution Operator S-Matrix Wick's Theorem FROM WICK EXPANSION TO FEYNMAN DIAGRAMS Yukawa Interaction: Decay of a Scalar Normalized States Sample Calculation of a Matrix Element Another Example: Fermion Scattering Feynman Amplitude Feynman Rules Virtual Particles Amplitudes which are not S-Matrix Elements CROSS SECTIONS AND DECAY RATES Decay Rate Example of Decay Rate Calculation Scattering Cross Section Generalities of 2-to-2 Scattering Inelastic Scattering with 4-Fermion Interaction Mandelstam Variables QUANTUM ELECTRODYNAMICS Local Gauge Invariance Interaction Hamiltonian Lower Order Processes Electron-Electron Scattering Electron-Positron Scattering e-e+®m-m+ Consequence of Gauge Invariance Compton Scattering Scattering by an External Field Bremmsstrahlung P, T, C, AND THEIR COMBINATIONS Motivations from Classical Physics Parity Charge Conjugation Time Reversal CP CPT ELECTROMAGNETIC FORM FACTORS General Electromagnetic Vertex Physical Interpretation of Form Factors Anomalous Magnetic Moment of the electron Charge Form Factor Electron-Proton Scattering RENORMALIZATION Degree of Divergence of a Diagram Specific Examples in QED Outline of the Program Ward-Takahashi Identity General Forms for Divergent Amplitudes Regularization of Self-Energy Diagrams Counterterms Full Lagrangian Observable Effects of Renormalization SYMMETRIES AND SYMMETRY BREAKING Classification of Symmetries Groups and Symmetries Approximate Symmetries Spontaneous Breaking of Symmetries Goldstone's Theorem Higgs Mechanism YANG-MILLS THEORY OF NON-ABELIAN GAUGE FIELDS Gauge Fields of Non-Abelian Symmetry Pure Gauge Lagrangian Interactions of Non-Abelian Gauge Fields Equations of Motion and Conserved Currents Quantization of Non-Abelian Gauge Fields Quantum Chromodynamics STANDARD ELECTROWEAK THEORY Gauge Group Spontaneous Symmetry Breaking Fermions in the Theory Gauge Boson Decay Scattering Processes Propagator for Unstable Particles Global Symmetries of the Model APPENDIX: Useful Formulas INDEX