Contents:
1. General Quantum Theory
[ps] 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] 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] 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] 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] 183
© 1996-2000
Institut
für Physik und Physikalische Technologien, TU Clausthal
Quantum Information Processing Group