|| Differential Geometry (differentiable manifold, metric, connection, curvature, geodesic, Lie derivative, Killing vector field), Einstein's fields equations, Lagrangian formulation, energy-momentum tensor, covariant conservation laws, gravitational waves, weak-field limit, Schwarzschild solution, Black holes, Kruskal coordinates, Reissner-Nordström solution, Kerr-Newman solution, homogenous and isotropic solution, Friedmann's equations, Hubble's law. ||Bartelmann (EN)
|| Scalar field, Noether's Theorem, canonical quantisation, Klein-Gordon equation, Fock space, vacuum energy, Schrödinger/Heisenberg picture, propagators, S-matrix, correlation functions, Wick's theorem, perturbation theory, Feynman diagrams, Feynman rules, cross sections, spin 1/2 fields, Dirac equation, spin 1 fields, QED, tree-level processes, renormalisation, Non-Abelian gauge theory, gauge symmetry, path integral quantisation, quantum effective action, background field method, RG, power counting, Yang-Mills theory, gauge fixing, Faddeev-Popov ghosts, BRST symmetry.
||Weigand (EN), Tong (EN), Dyson (EN)
|| Thermal quantum field theory (thermal field theory for free/interacting scalars, fermions and gauge fields, low-energy effective field theories, finite density, real-time observables), Non-equilibrium QFT (functional integral representation, initial conditions, 2PI effective action, evolution equations, thermal equilibrium, thermalization, expansion schemes, nonthermal fixed points, nonequilibrium instabilities),
QFT in curved backgrounds (Quantum fields in expanding universe/de Sitter spacetime, Unruh effect, Hawking radiation, thermodynamics of black holes, Casimir effect). ||Laine (EN), Berges (EN), Mukhanov (EN)
|| Homogeneous universe, Inhomogeneous universe, early universe, late universe, structure formation, expansion. ||Bartelmann (EN), Tong (EN)
|| Classical and quantum statistics, micro- and macrostates, partition function, statistical ensembles, equilibrium, entropy, principle of maximum entropy, thermodynamic potentials, ideal quantum gases, gas of interacting particles, phase transitions, critical phenomena. ||Tong (EN), Wegner (EN), Wetterich (EN), Schwarz (EN)
|| Finite group, Lie group, Lie algebra, SU(2), SO(N), SU(N), SU(3), Lorentz group, Poincaré group, conformal group, Non-Abelian gauge theories. ||Flörchinger (EN), Lüdeling (EN)