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.

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