An Elementary Primer For Gauge Theory

Description

An Elementary Primer For Gauge Theory......Page 1 Half-Title......Page 2 Title-Page......Page 4 Copyright......Page 5 Dedication......Page 6 Preface......Page 8 Contents......Page 10 Chapter I Introduction......Page 14 2.1 Introduction......Page 18 2.2 The Einstein Connection......Page 19 2.3 Weyl's Gauge Theory......Page 24 2.4 Canonical Momentum and Electrontagnetic Potential......Page 28 2.5 Quantum Mechanics and Gauge Theory......Page 29 2.6 The Aharonov-Bohm Effect......Page 31 2.7 Electromagnetism as a Gauge Theory......Page 34 2.8 Isotopic Spin and the New Gauge Theory......Page 35 2.9 Yang-Mills Gauge Theory......Page 38 2.10 Gauge Theory and Geometry......Page 42 2.11 Discussion......Page 45 3.1 Introduction......Page 47 3.2 Local Gauge Transfom1ations......Page 48 3.3 Connections and Potentials......Page 49 3.4 The Vector Potential Field......Page 52 3.5 Choosing a Gauge......Page 54 3.6 Maxwell's Field Tensor and Stoke's Theorem......Page 56 4.2 Building a Gauge Model......Page 61 4.3 The Problem of Mass......Page 64 4.4 The Yang-Mills Equations......Page 65 4.5 Particle Equation of Motion......Page 66 5.2 The Non-Abelian Divergence......Page 70 5.3 The Second Maxwell Equation and Charge Conservation......Page 74 5.4 Maxwell's Equations and Superposition......Page 78 5.5 Charges in Yang-Mills Theory......Page 79 5.6 Yang-Mills Wave Equation......Page 83 6.2 Leptons and W Bosons......Page 86 6.3 Quarks and Vveak Decays......Page 90 6.4 The "Dark Age" of Field Theory......Page 95 7.1 Introduction......Page 99 7.2 Symmetry Breaking of the Second Kind......Page 100 7.3 Geometry of Symmetry Breaking......Page 101 7.4 The Broken Gauge Superconductor......Page 106 7.5 Spontaneous Symmetry Breaking......Page 109 7.6 Goldstone's Theorem......Page 113 7.7 A Pa1·able about Symmetry Breaking......Page 114 8.1 Introduction......Page 115 8.2 Weak Interactions Revisited......Page 116 8.3 Unification without Renormalization......Page 119 8.4 Symmetry Breaking and Gauge Field Masses......Page 123 8.5 The Weinberg Angle......Page 124 8.6 Renormalization and Revival......Page 126 8.7 The Electron Mass......Page 130 8.8 Discussion......Page 131 9.1 Introduction......Page 134 9.2 Colored Quarks and Gluons......Page 135 9.3 Colorless Quark Systems......Page 137 9.4 Asymptotic Freedom......Page 140 9.5 The Running Coupling Constant......Page 143 9.6 Discussion......Page 149 10.1 Introduction......Page 152 10.2 Why Flux Trapping ?......Page 153 10.3 The Topological Superconductor......Page 154 10.4.1 Internal Space and Topology......Page 157 10.4.3 The Degenerate Vortex......Page 160 10.5 How to Add the Flux Number......Page 162 10.6 The Dirac Magnetic Monopole......Page 166 10.7 Discussion......Page 170 A.1 Continuous Groups......Page 171 A.2 Compact Lie Groups......Page 172 A.3 .1 Orthogonal Groups......Page 173 A.3.2 Special Unitary Groups......Page 174 A.3.3 Homomorphism of 0(3) and SU(2)......Page 175 A.4.1 Rotation Group......Page 177 A.4.2 Lie Group Generators......Page 178 A.5 The SU(3) Group......Page 179 Index......Page 182 Back Cover......Page 191