Contents
Preface v
Chapter 1. Prologue 1
1.1. Linguistic prologue: notation and terminology 1
1.2. Physical prologue: dimensions, units, constants, and particles 5
1.3. Mathematical prologue: some Lie groups and Lie algebras 8
Chapter 2. Review of Pre-quantum Physics 13
2.1. Mechanics according to Newton and Hamilton 13
2.2. Mechanics according to Lagrange 18
2.3. Special relativity 22
2.4. Electromagnetism 25
Chapter 3. Basic Quantum Mechanics 33
3.1. The mathematical framework 33
3.2. Quantization 42
3.3. Uncertainty inequalities 51
3.4. The harmonic oscillator 53
3.5. Angular momentum and spin 56
3.6. The Coulomb potential 60
Chapter 4. Relativistic Quantum Mechanics 65
4.1. The Klein-Gordon and Dirac equations 66
4.2. Invariance and covariance properties of the Dirac equation 70
4.3. Consequences of the Dirac equation 74
4.4. Single-particle state spaces 83
4.5. Multiparticle state spaces 89
Chapter 5. Free Quantum Fields 97
5.1. Scalar fields 97
5.2. The rigorous construction 105
5.3. Lagrangians and Hamiltonians 107
5.4. Spinor and vector fields 112
5.5. The Wightman axioms 119
Chapter 6. Quantum Fields with Interactions 123
6.1. Perturbation theory 123
6.2. A toy model for electrons in an atom 128
6.3. The scattering matrix 136
6.4. Evaluation of the S-matrix: first steps 143
6.5. Propagators 147
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