Preface
CHAPTER 1 Particle Physics and Special Relativity
Special Relativity
A Quick Overview of Particle Physics
Elementary Particles
The Higgs Mechanism
Grand Unification
Supersymmetry
String Theory
Summary
Quiz
CHAPTER 2 Lagrangian Field Theory
Basic Lagrangian Mechanics
The Action and the Equations of Motion
Canonical Momentum and the Hamiltonian
Lagrangian Field Theory
Symmetries and Conservation Laws
Conserved Currents
The Electromagnetic Field
Gauge Transformations
Summary
Quiz
CHAPTER 3 An Introduction to Group Theory
Representation of the Group
Group Parameters
Lie Groups
The Rotation Group
Representing Rotations
SO(N)
Unitary Groups
Casimir Operators
Summary
Quiz
CHAPTER 4 Discrete Symmetries and Quantum Numbers
Additive and Multiplicative Quantum Numbers
Parity
Charge Conjugation
CP Violation
The CPT Theorem
Summary
Quiz
CHAPTER 5 The Dirac Equation
The Classical Dirac Field
Adding Quantum Theory
The Form of the Dirac Matrices
Some Tedious Properties of the Dirac Matrices
Adjoint Spinors and Transformation Properties
Slash Notation
Solutions of the Dirac Equation
Free Space Solutions
Boosts, Rotations, and Helicity
Weyl Spinors
Summary
Quiz
CHAPTER 6 Scalar Fields
Arriving at the Klein-Gordon Equation
Reinterpreting the Field
Field Quantization of Scalar Fields
States in Quantum Field Theory
Positive and Negative Frequency Decomposition
Number Operators
Normalization of the States
Bose-Einstein Statistics
Normal and Time-Ordered Products
The Complex Scalar Field
Summary
Quiz
CHAPTER 7 The Feynman Rules
The Interaction Picture
Perturbation Theory
Basics of the Feynman Rules
Calculating Amplitudes
Steps to Construct an Amplitude
Rates of Decay and Lifetimes
Summary
Quiz
CHAPTER 8 Quantum Electrodynamics
Reviewing Classical Electrodynamics Again
The Quantized Electromagnetic Field
Gauge Invariance and QED
Feynman Rules for QED
Summary
Quiz
CHAPTER 9 Spontaneous Symmetry Breaking and the Higgs Mechanism
Symmetry Breaking in Field Theory
Mass Terms in the Lagrangian
Aside on Units
Spontaneous Symmetry Breaking and Mass
Lagrangians with Multiple Particles
The Higgs Mechanism
Summary
Quiz
CHAPTER 10 Electroweak Theory
Right- and Left-Handed Spinors
A Massless Dirac Lagrangian
Leptonic Fields of the Electroweak Interactions
Charges of the Electroweak Interaction
Unitary Transformations and the Gauge Fields of the Theory
Weak Mixing or Weinberg Angle
Symmetry Breaking
Giving Mass to the Lepton Fields
Gauge Masses
Summary
Quiz
CHAPTER 11 Path Integrals
Gaussian Integrals
Basic Path Integrals
Summary
Quiz
CHAPTER 12 Supersymmetry
Basic Overview of Supersymmetry
Supercharge
Supersymmetric Quantum Mechanics
The Simplified Wess-Zumino Model
A Simple SUSY Lagrangian
Summary
Quiz
Final Exam
Solutions to Quizzes and Final Exam
References
Index
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