An invitation to quantum field theory

✍ Scribed by Luis Alvarez-Gaumé; M A Vázquez-Mozo

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 307
• Series: Lecture notes in physics, v. 839
• Category: Library

✦ Synopsis

Why Do We Need Quantum Field Theory After All?.- From Classical to Quantum Fields.- Theories and Lagrangian I: Matter Fields.- Theories and Lagrangian II: Introducing Gauge Fields.- Theories and Lagrangian II: The Standard Model.- Towards Computational Rules: Feynman Diagrams.- Symmetries I: Continuous Symmetries.- Renormalization.- Anomalies.- The Origin of Mass.- Symmetries II: Discrete Symmetries.- Effective Field Theories and Naturalness.- Special Topics.- Notation, Conventions and Units.- A Crash Course in Group Theory.- Index

✦ Table of Contents

Cover......Page 1
An Invitation to Quantum
Field Theory......Page 4
ISBN 9783642237270......Page 5
Preface......Page 8
Contents......Page 10
1.1 Relativistic Quantum Mechanics......Page 14
1.2 The Klein Paradox......Page 17
1.3 From Wave Functions to Quantum Fields......Page 19
References......Page 21
2.1 Particles and Quantum Fields......Page 24
2.2 Canonical Quantization......Page 30
2.3 The Casimir Effect......Page 35
2.4 Path Integrals......Page 37
2.5 The Semiclassical Limit......Page 41
References......Page 45
3.1 Representations of the Lorentz Group......Page 46
3.2 Weyl Spinors......Page 49
3.3 Dirac Spinors......Page 51
4.1 Classical Gauge Fields......Page 60
The Aharonov--Bohm Effect......Page 62
Magnetic Monopoles......Page 64
4.2 Quantization of the Electromagnetic Field......Page 68
4.3 Coupling Gauge Fields to Matter......Page 69
4.4 Nonabelian Gauge Theories......Page 71
4.5 Understanding Gauge Symmetry......Page 74
Applications to Electrodynamics......Page 75
4.6 Gauge Fields and Path Integrals......Page 77
4.7 The Structure of the Gauge Theory Vacuum......Page 81
Subtleties and Technicalities......Page 87
4.8 Instantons in Gauge Theories......Page 88
References......Page 91
5.1 Fundamental Interactions......Page 94
5.2 Leptons and Quarks......Page 98
5.3 Quantum Chromodynamics......Page 103
5.4 The Electroweak Theory......Page 105
5.5 Closing Remarks: Particle Masses in the Standard Model......Page 111
References......Page 112
6.1 Cross Sections and S-Matrix Amplitudes......Page 114
6.2 From Green's Functions to Scattering Amplitudes......Page 122
6.3 Feynman Rules......Page 123
6.4 An Example: Compton Scattering at Low Energies......Page 129
6.5 Polarization of the Cosmic Microwave Background Radiation......Page 134
References......Page 139
8.1 Removing Infinities......Page 158
8.2 The Beta-Function and Asymptotic Freedom......Page 163
8.3 A Look at the Systematics of Renormalization......Page 168
8.4 Renormalization in Statistical Mechanics......Page 175
8.5 The Renormalization Group in Quantum Field Theory......Page 180
References......Page 185
9.1 A Toy Model for the Axial Anomaly......Page 188
9.2 The Triangle Diagram......Page 194
9.3 Chiral Symmetry in QCD......Page 196
9.4 Gauge Anomalies......Page 202
References......Page 205
10.1 The Masses in the Standard Model......Page 206
10.2 Quark Masses......Page 215
10.3 ΛQCD and the Hadron Masses......Page 217
References......Page 221
11.1 Discrete Symmetries in Classical Mechanics and Field Theory......Page 222
11.2 Parity and Charge Conjugation in Quantum Field Theory......Page 226
11.3 Majorana Spinors......Page 228
11.4 Time Reversal......Page 229
11.5 CP Symmetry and CP Violation......Page 232
11.6 The CPT Theorem......Page 235
The Proof......Page 238
Implications of the Theorem......Page 241
11.7 Spin and Statistics......Page 242
References......Page 243
12.1 Energy Scales in Quantum Field Theory......Page 244
12.2 Dimensional Regularization......Page 245
12.3 The d楳灬慹敱 㴀七였㐀  吀栀攀漀爀礀㨀 䄀 䌀愀猀攀 匀琀甀搀......Page 249
12.4 The Renormalization Group Equations in Dimensional Regularization......Page 257
12.5 The Issue of Quadratic Divergences......Page 260
12.6 Effective Field Theories: A Brief Introduction......Page 262
12.7 Remarks on Naturalness......Page 268
12.8 Coda: Heavy Particles and Decoupling......Page 270
References......Page 273
Particle Creation by a Classical Source......Page 274
The Schwinger Effect......Page 277
13.2 Supersymmetry......Page 281
References......Page 286
A.1 Covariant Notation......Page 288
A.3 Units......Page 289
B.1 Generalities......Page 290
B.2 Lie Groups and Lie Algebras......Page 291
B.3 Invariants......Page 295
B.4 A Look at the Lorentz and Poincaré Groups......Page 296
References......Page 301
Index......Page 302