` Thermal Field Theory W 2023/24

Thermal Field Theory

Dietrich Bödeker

Lecture notes, problem sheets

  1. Outline
    1 Ideal gas
  2. 2 Scalar field theory 2.1 Path integral for Z
    Sheet 1
  3. Path intergral version #1
    2.2 Perturbation theory
  4. 2.3 High-temperature expansion, Matsubara sums
    Sheet 2
  5. 2.4 Interacting field
  6. 2.5 Renormalization at order lambda
    Sheet 3
  7. 2.6 Infrared divergences
  8. 2.7 Infrared resummation
    Sheet 4
  9. 3. Fermions 3.1 Path integral
  10. 3.2 Matsubara sum 3.3 Dirac field, Wick's theorem 4 Gauge fields 4.1 Gauge invariance
    Sheet 5
  11. 4.2 Canonical formulation 4.3 Path integral
  12. 4.4 Gauge field propagator 5 Quantum electrodynamics (QED) 5.1 Ideal gas pressure 5.2 Order e² corrections
    Sheet 6
  13. 5.3 Photon polarisation tensor
  14. 5.4 QED pressure at order e³ 6 Non-abelian gauge fields 6.1 Gauge transformations 6.2 Fadeev-Popov ghosts
    Sheet 7
  15. 6.3 Gluon polarization tensor: gluon self-interactions
  16. 6.4 Gluon polarization tensor: ghosts, fermions
    Sheet 8
  17. 6.5 Debye mass 7 Dimensional reduction 7.1 The Linde problem
  18. 7.2 Effective 3-dimensional theories
    Sheet 9
  19. 7.3 Phase transitions
    Sheet 10
  20. 8 Real-time correlations 8.1 Correlation functions 8.2 Particle production
  21. 8.3 Relating correlation functions
    Sheet 11
  22. Supplement: chiral fermions,
    8.4 Production of sterile neutrinos
  23. 8.5 Computation of the production rate
    Sheet 12
  24. 8.6 Fermion selfenergy, HTL approximation
    • mathematica notebook for Matsubara sums
  25. 8.7 HTL-resummed fermion propagator, 8.8 HTL polarization tensor
    Sheet 13
  26. 8.9 Hard thermal loops and kinetic equations
  27. 8.10 Non-abelian hard thermal loops, perturbation theory, size of field fluctuations
    Sheet 14
    • Analytic continuation from Matsubara frequencies: Baym, Mermin, Determination of Thermodynamic Green's Functions
  28. 8.11 Effects of hard thermal loops
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