Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Notation -- 1 Introduction -- 1.1 Overview -- 1.2 Typical Scales in High-energy Physics -- Further Reading -- Exercises -- 2 Lorentz and Poincare Symmetries in QFT -- 2.1 Lie Groups -- 2.2 The Lorentz Group -- 2.3 The Lorentz Algebra -- 2.4 Tensor Representations -- 2.4.1 Decomposition of Lorentz Tensors Under SO(3) -- 2.5 Spinorial Representations -- 2.5.1 Spinors in Non-Relativistic Quantum Mechanics -- 2.5.2 Spinors in the Relativistic Theory -- 2.6 Field Representations -- 2.6.1 Scalar Fields -- 2.6.2 Weyl Fields -- 2.6.3 Dirac Fields -- 2.6.4 Majorana Fields -- 2.6.5 Vector Fields -- 2.7 The Poincare Group -- 2.7.1 Representation on Fields -- 2.7.2 Representation on One-particle States -- Summary of Chapter -- Further Reading -- Exercises -- 3 Classical Field Theory -- 3.1 The Action Principle -- 3.2 Noether's Theorem -- 3.2.1 The Energy-momentum Tensor -- 3.3 Scalar Fields -- 3.3.1 Real Scalar Fields -- Klein-Gordon Equation -- 3.3.2 Complex Scalar field -- U(1) Charge -- 3.4 Spinor Fields -- 3.4.1 The Weyl Equation -- Helicity -- 3.4.2 The Dirac Equation -- 3.4.3 Chiral Symmetry -- 3.4.4 Majorana Mass -- 3.5 The Electromagnetic Field -- 3.5.1 Covariant form of The Free Maxwell Equations -- 3.5.2 Gauge Invariance -- Radiation and Lorentz Gauges -- 3.5.3 The Energy-momentum Tensor -- 3.5.4 Minimal and Non-minimal Coupling to Matter -- 3.6 First Quantization of Relativistic Wave Equations -- 3.7 Solved Problems -- The Fine Structure of the Hydrogen Atom -- Relativistic Energy Levels in a Magnetic Field -- Summary of Chapter -- Exercises -- 4 Quantization of Free Fields -- 4.1 Scalar Fields -- 4.1.1 Real Scalar Fields. Fock space -- 4.1.2 Complex Scalar field -- Antiparticles -- 4.2 Spin 1/2 Fields -- 4.2.1 Dirac Field -- 4.2.2 Massless Weyl field.

4.2.3 C, P, T -- 4.3 Electromagnetic Field -- 4.3.1 Quantization in the Radiation Gauge -- 4.3.2 Covariant Quantization -- Summary of Chapter -- Exercises -- 5 Perturbation Theory and Feynman Diagrams -- 5.1 The S-matrix -- 5.2 The LSZ Reduction Formula -- 5.3 Setting up the Perturbative Expansion -- 5.4 The Feynman Propagator -- 5.5 Wick's Theorem and Feynman Diagrams -- 5.5.1 A Few very Explicit Computations -- 5.5.2 Loops and Divergences -- 5.5.3 Summary of Feynman Rules for a Scalar Field -- 5.5.4 Feynman Rules for Fermions and Gauge Bosons -- 5.6 Renormalization -- 5.7 Vacuum Energy and the Cosmological Constant Problem -- 5.8 The Modern Point of view on Renormalizability -- 5.9 The Running of Coupling Constants -- Summary of Chapter -- Further Reading -- Exercises -- 6 Cross-sections and Decay Rates -- 6.1 Relativistic and Non-relativistic Normalizations -- 6.2 Decay rates -- 6.3 Cross-sections -- 6.4 Two-body Final States -- 6.5 Resonances and the Breit-Wigner Distribution -- 6.6 Born Approximation and Non-relativistic Scattering -- 6.7 Solved Problems -- Three-body kinematics and Phase Space -- Inelastic Scattering of Non-relativistic Electrons on Atoms -- Summary of Chapter -- Further Reading -- Exercises -- 7 Quantum Electrodynamics -- 7.1 The QED Lagrangian -- 7.2 One-loop Divergences -- 7.3 Solved Problems -- e+ e- -> γ -> μ+ μ- -- Electromagnetic form Factors -- Summary of Chapter -- Further Reading -- Exercises -- 8 The Low-energy Limit of the Electroweak Theory -- 8.1 A Four-Fermion Model -- 8.2 Charged and Neutral Currents in the Standard Model -- 8.3 Solved Problems: Weak Decays -- μ- -> e-ve vμ -- Isospin and Flavor SU(3) -- K0 -> π- l+ vl -- Summary of Chapter -- Further Reading -- Exercises -- 9 Path Integral Quantization -- 9.1 Path Integral Formulation of Quantum Mechanics -- 9.2 Path Integral Quantization of Scalar Fields.

9.3 Perturbative Evaluation of the path Integral -- 9.4 Euclidean Formulation -- 9.5 QFT and Critical Phenomena -- 9.6 QFT at Finite Temperature -- 9.7 Solved Problems -- Instantons and Tunneling -- Summary of Chapter -- Further Reading -- 10 Non-Abelian Gauge Theories -- 10.1 Non-Abelian Gauge Transformations -- 10.2 Yang-Mills Theory -- 10.3 QCD -- 10.4 Fields in the Adjoint Representation -- Summary of Chapter -- Further Reading -- 11 Spontaneous Symmetry Breaking -- 11.1 Degenerate Vacua in QM and QFT -- 11.2 SSB of Global Symmetries and Goldstone Bosons -- 11.3 Abelian Gauge Theories: SSB and Superconductivity -- 11.4 Non-abelian Gauge Theories: the Masses of W± and Z0 -- Summary of Chapter -- Further Reading -- 12 Solutions to Exercises -- 12.1 Chapter 1 -- 12.2 Chapter 2 -- 12.3 Chapter 3 -- 12.4 Chapter 4 -- 12.5 Chapter 5 -- 12.6 Chapter 6 -- 12.7 Chapter 7 -- 12.8 Chapter 8 -- Bibliography -- Index.