Title Page, Preface and Table of Contents [ps][pdf] | |
1. General Quantum Theory [ps][pdf] | 5 |
1.1. Basic Logical Structure | 5 |
1.1.1. Classical Logic and General Notions | 5 |
1.1.2. Quantum Logic | 6 |
1.1.3. Quantum Reasoning | 8 |
1.1.4. Symmetries and Dynamics | 12 |
1.2. Orthodox Quantum Mechanics | 13 |
1.2.1. Logic and Observables | 13 |
1.2.2. Symmetries and Dynamics | 17 |
1.2.3. Algebras of Bounded Observables | 18 |
1.2.4. State Functionals | 19 |
1.3. Algebraic Formulation of General Quantum Theory | 22 |
1.3.1. Partial States | 22 |
1.3.2. GNS-Representation | 25 |
1.3.3. Canonical Quantization | 27 |
1.3.4. Spontaneously Broken Symmetries | 32 |
2. Massive Scalar Fields [ps][pdf] | 35 |
2.1. Free Neutral Scalar Fields | 35 |
2.1.1. 1-Particle Space | 35 |
2.1.2. Fock Space | 41 |
2.1.3. The Free Field | 44 |
2.2. Wightman Theory for Neutral Scalar Fields | 49 |
2.2.1. Wightman Axioms | 49 |
2.2.2. Remarks on the Choice of the Space of Test Functions | 51 |
2.2.3. Mathematical Tools | 52 |
2.2.4. Some Standard Results | 57 |
2.2.5. PCT Theorem | 67 |
2.3. S-Matrix for Self-Interacting Neutral Scalar Fields | 69 |
2.3.1. General Scattering Theory | 69 |
2.3.2. Asymptotic Condition for Massive Neutral Scalar Particles | 72 |
2.3.3. Evaluation of the Asymptotic Condition | 76 |
2.3.4. Cluster Properties of the S-Matrix | 83 |
2.4. Charged Scalar Fields | 87 |
2.4.1. Free Charged Scalar Fields | 87 |
2.4.2. Wightman Theory for Charged Scalar Fields | 88 |
2.4.3. Scattering Theory | 93 |
3. Perturbation Theory [ps][pdf] | 95 |
3.1. General Aspects | 95 |
3.1.1. Interaction Picture | 95 |
3.1.2. Canonical Field Quantization | 98 |
3.2. Canonical Perturbation Theory | 104 |
3.2.1. Dyson Series and Wick's Theorem | 104 |
3.2.2. Counter Terms and Renormalization | 104 |
3.2.3. Feynman Rules | 109 |
3.3. Bogoliubov-Shirkov Theory | 116 |
3.3.1. Basic Assumptions | 116 |
3.3.2. General Solution | 120 |
3.3.3. Generalization to Nonlocalizable Test Spaces | 124 |
4. Quantum Electrodynamics [ps][pdf] | 133 |
4.1. The Free Electromagnetic Field Operators | 133 |
4.1.1. Wightman Theory | 133 |
4.1.2. Problems With the Quantized Potentials | 135 |
4.1.3. Gupta-Bleuler Construction | 138 |
4.1.4. Gupta-Bleuler Observables | 142 |
4.2. The Quantized Free Dirac Field | 147 |
4.2.1. Lorentz Transformations Characterized via Complex 2-2-Matrices | 147 |
4.2.2. Relativistic Covariance in General | 151 |
4.2.3. Dirac Particles | 152 |
4.2.4. Quantized Dirac Field | 162 |
4.3. The S-Matrix of Quantum Electrodynamics (QED) | 167 |
4.3.1. Naive Interaction Picture of QED | 168 |
4.3.2. General Perturbation Theory | 171 |
4.3.3. The Feynman Rules of QED | 175 |
4.3.4. Example: Compton Scattering | 178 |
References [ps][pdf] | 183 |
Last Changes: April 17, 2001 by Wolfgang Lücke