Quantum Field Theory Demystified

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ISBN: 9780071543828 | 0071543821
Cover: Paperback
Copyright: 3/21/2008

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Learn quantum field theory at the speed of light! Quantum Field Theory Demystified picks up where Quantum Mechanics Demystified left off and is the ideal introductory resource for those moving onto this complex physics course. Quantum field theory unifies Einstein's theory of relativity with quantum mechanics. You will learn the essential principles and mathematical framework of quantum field theory through easy-to-follow explanations and sample equations. The book also provides the background needed to learn more advanced topics such as string theory, supersymmetry, and quantum gravity.

Preface	p. xv
Particle Physics and Special Relativity	p. 1
Special Relativity	p. 5
A Quick Overview of Particle Physics	p. 12
Elementary Particles	p. 14
The Higgs Mechanism	p. 18
Grand Unification	p. 18
Supersymmetry	p. 19
String Theory	p. 19
Summary	p. 20
Quiz	p. 20
Lagrangian Field Theory	p. 23
Basic Lagrangian Mechanics	p. 23
The Action and the Equations of Motion	p. 26
Canonical Momentum and the Hamiltonian	p. 29
Lagrangian Field Theory	p. 30
Symmetries and Conservation Laws	p. 35
Conserved Currents	p. 38
The Electromagnetic Field	p. 39
Gauge Transformations	p. 43
Summary	p. 47
Quiz	p. 47
An Introduction to Group Theory	p. 49
Representation of the Group	p. 50
Group Parameters	p. 52
Lie Groups	p. 52
The Rotation Group	p. 54
Representing Rotations	p. 55
SO(N)	p. 58
Unitary Groups	p. 62
Casimir Operators	p. 67
Summary	p. 68
Quiz	p. 68
Discrete Symmetries and Quantum Numbers	p. 71
Additive and Multiplicative Quantum Numbers	p. 71
Parity	p. 72
Charge Conjugation	p. 76
CP Violation	p. 78
The CPT Theorem	p. 80
Summary	p. 82
Quiz	p. 83
The Dirac Equation	p. 85
The Classical Dirac Field	p. 85
Adding Quantum Theory	p. 87
The Form of the Dirac Matrices	p. 89
Some Tedious Properties of the Dirac Matrices	p. 91
Adjoint Spinors and Transformation Properties	p. 94
Slash Notation	p. 95
Solutions of the Dirac Equation	p. 95
Free Space Solutions	p. 99
Boosts, Rotations, and Helicity	p. 103
Weyl Spinors	p. 104
Summary	p. 107
Quiz	p. 108
Scalar Fields	p. 109
Arriving at the Klein-Gordon Equation	p. 110
Reinterpreting the Field	p. 117
Field Quantization of Scalar Fields	p. 117
States in Quantum Field Theory	p. 127
Positive and Negative Frequency Decomposition	p. 128
Number Operators	p. 128
Normalization of the States	p. 130
Bose-Einstein Statistics	p. 131
Normal and Time-Ordered Products	p. 134
The Complex Scalar Field	p. 135
Summary	p. 137
Quiz	p. 137
The Feynman Rules	p. 139
The Interaction Picture	p. 141
Perturbation Theory	p. 143
Basics of the Feynman Rules	p. 146
Calculating Amplitudes	p. 151
Steps to Construct an Amplitude	p. 153
Rates of Decay and Lifetimes	p. 160
Summary	p. 160
Quiz	p. 160
Quantum Electrodynamics	p. 163
Reviewing Classical Electrodynamics Again	p. 165
The Quantized Electromagnetic Field	p. 168
Gauge Invariance and QED	p. 170
Feynman Rules for QED	p. 173
Summary	p. 185
Quiz	p. 185
Spontaneous Symmetry Breaking and the Higgs Mechanism	p. 187
Symmetry Breaking in Field Theory	p. 189
Mass Terms in the Lagrangian	p. 192
Aside on Units	p. 195
Spontaneous Symmetry Breaking and Mass	p. 196
Lagrangians with Multiple Particles	p. 199
The Higgs Mechanism	p. 202
Summary	p. 207
Quiz	p. 207
Electroweak Theory	p. 209
Right- and Left-Handed Spinors	p. 210
A Massless Dirac Lagrangian	p. 211
Leptonic Fields of the Electroweak Interactions	p. 212
Charges of the Electroweak Interaction	p. 213
Unitary Transformations and the Gauge Fields of the Theory	p. 215
Weak Mixing or Weinberg Angle	p. 219
Symmetry Breaking	p. 220
Giving Mass to the Lepton Fields	p. 222
Gauge Masses	p. 224
Summary	p. 231
Quiz	p. 231
Path Integrals	p. 233
Gaussian Integrals	p. 233
Basic Path Integrals	p. 238
Summary	p. 242
Quiz	p. 243
Supersymmetry	p. 245
Basic Overview of Supersymmetry	p. 246
Supercharge	p. 247
Supersymmetric Quantum Mechanics	p. 249
The Simplified Wess-Zumino Model	p. 253
A Simple SUSY Lagrangian	p. 254
Summary	p. 260
Quiz	p. 260
Final Exam	p. 263
Solutions to Quizzes and Final Exam	p. 281
References	p. 289
Index	p. 291
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Quantum Field Theory Demystified

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