Quantum Field Theory

Dietrich Bödeker

Lecture notes, problem sheets

  1. Why Quantum Field Theory?
    1 Classical field theory, symmetries 1.1 Principle of least action 1.2 Lorentz invariance
    Sheet 1
  2. 1.3 Hamiltonian formulation, 1.4 Noether's theorem
  3. 1.5 Complex Klein-Gordon field, 1.6 Poisson brackets, symmetry generators
    Sheet 2
  4. 2 Scalar field quantization 2.1 Canonical quantization 2.2 Quantized real scalar field
  5. 2.3 Particles, spin, statistics 2.4 Complex scalar field
    Sheet 3
  6. 2.5 Finite symmetry transformations 3 Correlation functions, interactions and scattering 2.1 Two-point functions, 2.2 Interactions
  7. 2.3 Energy spectrum, 2.4 Propagator
  8. 2.5 In and out states 2.6 Normalizable 1-particle states
    Sheet 4
  9. 2.7 Lehmann-Symanzik-Zimmermann formula 2.8 Cross sections
  10. 3. Path integrals 3.1 Generating functional for n-point functions 3.2 Path integrals 3.3 Path integral for the generating functional
    Sheet 5
  11. 3.4 Generating functional for free fields 3.5 Interactions, perturbation theory
  12. 3.6 Normalization factor 3.7 Two-point function at order lambda
    Sheet 6
  13. 3.8 Four-point function at order lambda 3.9 Feynman rules
  14. 4 Renormalization 4.1 Full propagator 4.2 Counting divergenes 4.3 Regularization
    Sheet 7
  15. 4.4 Dimensional regularization, 4.5 Mass renormalization
  16. 4.6 Four point function 4.7 Coupling constant renormalization
    Sheet 8
  17. 4.8 Minimal subtraction 4.9 Renormalization group
  18. 4.10 Asymptotic behavior
    Supplement: Lie algebras
  19. 5. Spin 1/2 fields and particles 5.1 Spinors
    Sheet 9
  20. 5.3 Scalars and vectors built from spinors 5.4 Free Dirac equation
    Sheet 10
  21. 5.5 Quantization, spin and statistics 5.6 Path integrals for fermions
  22. 5.7 Path integral for Dirac field, LSZ for Dirac fermions 6 Gauge fields 6.1 Canonical formulation
  23. 6.2 Path integral 6.4 Feynman propagator
    Sheet 11
  24. 7 Quantum elelectrodynamics 7.1 Gauge invariance 7.2 Perturbation theory
    Sheet 12
  25. 7.3 mu+ mu- pair creation
    Supplement: spin sums
    Sheet 13
  26. 7.4 Non-relativistic limit
  27. 7.5 Higher orders: vertex corrections
  28. 7.6 Vertex corrections at order α
    Mathematica notebook
    Sheet 14
  29. 7.7 The anomalous magnetic moment

Literature, (some online books accessible only in the Uni VPN, see also Semesterapparat in the library)