Digestible Quantum Field Theory (eBook)

Menu 6
Part I Aperitif 10
1 Introduction 11
2 Units Fundamental Constants Conventions 16
Part II Hors d'Oeuvres 21
3 The Universe as We Know It 22
3.1 Elementary Particles 23
3.2 Gravitational Interaction 26
3.3 Electromagnetic Interactions 27
3.4 Strong Interactions 29
3.5 Weak Interactions 32
4 The Cubic Edifice of Physical Theories 35
4.1 Classical Mechanics 35
4.2 Relativistic Mechanics 36
4.3 Quantum Mechanics 38
4.4 Relativistic Quantum Mechanics 41
4.5 Nonrelativistic Field Theory 46
4.6 Relativistic Field Theory 48
4.7 Quantum Field Theory 50
4.8 Not in the Cube 59
5 Genesis of the Standard Model 61
5.1 Trees 61
5.2 Loops Feynman Technique Divergences and Renormalization 66
5.3 From Nuclei to Gluon Jets 71
5.4 From ? Decay to the Higgs Boson 80
Part III Chef's Secrets 91
6 Groups and Algebras 92
6.1 Scalars Vectors Tensors 92
6.1.1 Euclidean Space 92
6.1.2 Minkowski Space 94
6.2 Finite Groups 96
6.3 Lie Groups 97
6.3.1 Orthogonal Groups 97
6.3.2 Lorentz Group 100
6.3.3 Unitary Groups 101
6.3.4 Representations 103
6.4 Grassmann Algebra 108
7 Lagrangians and Hamiltonians 110
7.1 Nonrelativistic Mechanics 110
7.2 Lorentz Force 114
7.3 Field Theories 117
8 Cross Sections and Amplitudes 126
8.1 Kinematics 126
8.2 Born Approximation and Beyond 130
8.3 Path Integrals 136
Part IV Entrées 143
9 Fermion Fields 144
9.1 First Try 145
9.2 Grassmann Waves in the Dirac Sea 148
9.3 Electromagnetic Interactions Dirac Equation 153
10 Feynman Graphs 159
10.1 Kinematics 159
10.2 Potential Scattering 161
10.3 Scalar Field Theory 163
10.4 Scalar Electrodynamics 164
10.5 Spinor Electrodynamics 168
10.6 Loops 171
11 Quantum Chromodynamics 177
11.1 QCD Lagrangian 177
11.2 Feynman Rules Asymptotic Freedom Confinement 180
11.3 November Revolution and Quarkonium 185
11.4 Light Mesons and Baryons 191
11.5 Chiral Symmetry and Its Breaking 197
11.5.1 Chiral Symmetry in QCD 197
11.5.2 Spontaneous Symmetry Breaking Goldstone's Theorem 199
11.5.3 Quark Condensate Pseudoscalar Pseudogoldstones 203
11.6 Hadron Masses Baryon Magnetic Moments 207
12 Theory of the Electroweak Interactions 210
12.1 Fermi Theory Weak Currents 210
12.2 Higgs Mechanism 216
12.2.1 Abelian 216
12.2.2 Non-Abelian 218
12.3 Standard Model: Gauge and Higgs Sectors 220
12.4 Standard Model: Fermions 222
12.4.1 Gauge Interactions 222
12.4.2 Masses 226
12.4.3 Generations and Their Mixing 228
12.5 Back to the Zoo 229
12.6 Neutrino Oscillations 233
12.7 Complaints and Outlook 236
12.7.1 Complaining 236
12.7.2 Looking Through the Supersymmetric Window 238
Part V Trou Normand 241
13 The Human Dimension 242
13.1 Richard Feynmanaut]Feynman, Richard|( 242
13.1.1 Safecracker 243
13.1.2 Drum Player 244
13.1.3 Artist 246
13.2 Lev Landauaut]Landau, Lev|( 247
13.2.1 Youth 249
13.2.2 Kharkov Landau's Minimum 250
13.2.3 Arrest The Bomb 252
13.2.4 Accident 254
13.3 Karen Ter-Martirosyan ITEP 255
Part VI Dessert 259
14 Supersymmetry 260
14.1 Electrons in a Magnetic Field 262
14.2 Grassmannian Description 267
14.3 Field Theories 270
14.4 The Case for Supersymmetry 276
15 General Relativity 282
15.1 Curved Space-Time 283
15.1.1 Mathematics 283
15.1.2 Physics 287
15.2 Actions Equations of Motion Their Solutions 290
15.2.1 Gravitational Waves 292
15.2.2 Schwarzschild Solution and Black Holes 294
15.2.3 Friedmann Solution and Cosmology 296
16 Mysterious Quantum Gravity 1
16.1 Attempts at Perturbative Calculations 303
16.1.1 Graviton Scattering 303
16.1.2 What Is Wrong with Non-renormalizability? 305
16.1.3 Supergravity 309
16.2 Breaking of Causality Hawking Paradox 311
16.3 Strings 316
16.3.1 Bosonic Strings 316
16.3.2 Superstrings 320
16.3.3 New Complaints 321
16.4 Author's Sweet Dreams 322
16.4.1 The Universe as a Soap Bubble 322
16.4.2 Living with Ghosts 325
Part VII Coffee 330
17 Recommended Reading 331
Appendix Subject Index 334
Index 334
Appendix Name Index 340
Author Index 340