Quantum Field Theory

1.1.1 Classical Logic and General Notions......Page 7
1.1.2 Quantum Logic......Page 8
1.1.3 Quantum Reasoning......Page 11
1.1.4 Symmetries and Dynamics......Page 14
1.2.1 Logic and Observables......Page 15
1.2.2 Symmetries and Dynamics......Page 19
1.2.3 Algebras of Bounded Observables......Page 20
1.2.4 State Functionals......Page 22
1.3.1 Partial States......Page 24
1.3.2 GNS-Representation......Page 27
1.3.3 Canonical Quantization......Page 30
1.3.4 Spontaneously Broken Symmetries......Page 35
2.1.1 1-Particle Space......Page 39
2.1.2 Fock Space......Page 45
2.1.3 The Free Field......Page 48
2.2.1 Wightman Axioms......Page 54
2.2.2 Remarks on the Choice of the Space of Test Functions......Page 56
2.2.3 Mathematical Tools......Page 57
2.2.4 Some Standard Results......Page 62
2.2.5 PCT Theorem......Page 72
2.3.1 General Scattering Theory......Page 75
2.3.2 Asymptotic condition for massive neutral scalar particles......Page 78
2.3.3 Evaluation of the Asymptotic Condition......Page 81
2.3.4 Cluster Properties of the S-Matrix......Page 89
2.4.1 Free Charged Scalar Fields......Page 93
2.4.2 Wightman Theory for Charged Scalar Fields......Page 94
2.4.3 Scattering Theory......Page 99
3.1.1 Interaction Picture......Page 101
3.1.2 Canonical Field Quantization......Page 104
3.2.1 Dyson Series and Wick\'s Theorem......Page 110
3.2.2 Counter Terms and Renormalization......Page 116
3.2.3 Feynman Rules......Page 120
3.3.1 Basic Assumptions......Page 123
3.3.2 General Solution......Page 127
3.3.3 Generalization to Nonlocalizable Test Spaces......Page 131
4.1.1 Wightman Theory......Page 139
4.1.2 Problems With the Quantized Potentials......Page 141
4.1.3 Gupta-Bleuler Construction......Page 144
4.1.4 Gupta-Bleuler Observables......Page 149
4.2.1 Lorentz Transformations......Page 153
4.2.2 Relativistic Covariance in General......Page 157
4.2.3 Dirac Particles......Page 159
4.2.4 Quantized Dirac Field......Page 168
4.3.1 Naive Interaction Picture of QED......Page 174
4.3.2 General Perturbation Theory......Page 177
4.3.3 The Feynman Rules of QED......Page 180
4.3.4 Compton Scattering......Page 185
Bibliography......Page 191