Quantum Field Theory Demystified
Learn quantum field theory relatively easily\ Trying to comprehend quantum field theory but don't have infinite time or the IQ of Einstein? No problem! This easy-to-follow guide helps you understand this complex subject matter without spending a lot of energy.\ Quantum Field Theory Demystified covers essential principles such as particle physics and special relativity. You'll learn about Lagrangian field theory, group theory, and electroweak theory. The book also explains continuous and...
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Learn quantum field theory relatively easilyTrying to comprehend quantum field theory but don't have infinite time or the IQ of Einstein? No problem! This easy-to-follow guide helps you understand this complex subject matter without spending a lot of energy. Quantum Field Theory Demystified covers essential principles such as particle physics and special relativity. You'll learn about Lagrangian field theory, group theory, and electroweak theory. The book also explains continuous and discrete symmetries, spontaneous symmetry breaking, and supersymmetry. With thorough coverage of the mathematics of quantum field theory and featuring end-of-chapter quizzes and a final exam to test your knowledge, this book will teach you the fundamentals of this theoretical framework in no time at all. This fast and easy guide offers:Numerous figures to illustrate key conceptsSample equations with worked solutionsCoverage of quantum numbersDetails on the Dirac equation, the Feynman rules, and the Higgs mechanismA time-saving approach to performing better on an exam or at workSimple enough for a beginner, but challenging enough for an advanced student, Quantum Field Theory Demystified is your shortcut to understanding this fascinating area of physics.
Preface xvParticle Physics and Special Relativity 1Special Relativity 5A Quick Overview of Particle Physics 12Elementary Particles 14The Higgs Mechanism 18Grand Unification 18Supersymmetry 19String Theory 19Summary 20Quiz 20Lagrangian Field Theory 23Basic Lagrangian Mechanics 23The Action and the Equations of Motion 26Canonical Momentum and the Hamiltonian 29Lagrangian Field Theory 30Symmetries and Conservation Laws 35Conserved Currents 38The Electromagnetic Field 39Gauge Transformations 43Summary 47Quiz 47An Introduction to Group Theory 49Representation of the Group 50Group Parameters 52Lie Groups 52The Rotation Group 54Representing Rotations 55SO(N) 58Unitary Groups 62Casimir Operators 67Summary 68Quiz 68Discrete Symmetries and Quantum Numbers 71Additive and Multiplicative Quantum Numbers 71Parity 72Charge Conjugation 76CP Violation 78The CPT Theorem 80Summary 82Quiz 83The Dirac Equation 85The Classical Dirac Field 85Adding Quantum Theory 87The Form of the Dirac Matrices 89Some Tedious Properties of the Dirac Matrices 91Adjoint Spinors and Transformation Properties 94Slash Notation 95Solutions of the Dirac Equation 95Free Space Solutions 99Boosts, Rotations, and Helicity 103Weyl Spinors 104Summary 107Quiz 108Scalar Fields 109Arriving at the Klein-Gordon Equation 110Reinterpreting the Field 117Field Quantization of Scalar Fields 117States in Quantum Field Theory 127Positive and Negative Frequency Decomposition 128Number Operators 128Normalization of the States 130Bose-Einstein Statistics 131Normal and Time-Ordered Products 134The Complex Scalar Field 135Summary 137Quiz 137The Feynman Rules 139The Interaction Picture 141Perturbation Theory 143Basics of the Feynman Rules 146Calculating Amplitudes 151Steps to Construct an Amplitude 153Rates of Decay and Lifetimes 160Summary 160Quiz 160Quantum Electrodynamics 163Reviewing Classical Electrodynamics Again 165The Quantized Electromagnetic Field 168Gauge Invariance and QED 170Feynman Rules for QED 173Summary 185Quiz 185Spontaneous Symmetry Breaking and the Higgs Mechanism 187Symmetry Breaking in Field Theory 189Mass Terms in the Lagrangian 192Aside on Units 195Spontaneous Symmetry Breaking and Mass 196Lagrangians with Multiple Particles 199The Higgs Mechanism 202Summary 207Quiz 207Electroweak Theory 209Right- and Left-Handed Spinors 210A Massless Dirac Lagrangian 211Leptonic Fields of the Electroweak Interactions 212Charges of the Electroweak Interaction 213Unitary Transformations and the Gauge Fields of the Theory 215Weak Mixing or Weinberg Angle 219Symmetry Breaking 220Giving Mass to the Lepton Fields 222Gauge Masses 224Summary 231Quiz 231Path Integrals 233Gaussian Integrals 233Basic Path Integrals 238Summary 242Quiz 243Supersymmetry 245Basic Overview of Supersymmetry 246Supercharge 247Supersymmetric Quantum Mechanics 249The Simplified Wess-Zumino Model 253A Simple SUSY Lagrangian 254Summary 260Quiz 260Final Exam 263Solutions to Quizzes and Final Exam 281References 289Index 291
