# Study Tips

## Open source lecture notes

Below you can find a few recommendations of open source lecture notes. I own

### Basic lectures in theoretical physics

Lecture | Contents | Notes |
---|---|---|

I | Basics of theoretical physics: Newton's axioms, harmonic oscillator, differential equations, vector fields, conservative forces, curvilinear coordinates, Taylor series, complex numbers, Newtonian gravity, Kepler problem, divergence theorem, Stokes' theorem, groups and matrices, Galilean transformations. | Bartelmann (DE), Tong (EN) |

II | Analytical mechanics: Mechanical constraints, Euler-Lagrange equation, Hamilton's principle, symmetries and conservation laws, Noether's theorem, rigid bodies, Poisson brackets, phase space, Liouville's theorem, chaotic systems, partial differential equations, Thermodynamics & Statistical physics: Ensembles, statistics, ideal gas, diffusion, Boltzmann distribution, Legendre transformations, differentials, temperature, entropy, heat, fundamental laws of thermodynamics, Carnot cycle, thermodynamic potentials, phase transitions. | Bartelmann (DE), Tong (EN) |

III | Electrodynamics: Maxwell's equations, electrostatics, magnetostatics, multipole expansion, spherical harmonics, Fourier analysis, Fourier integrals, Maxwell's equations in matter, particles and fields, waves, waves in matter, fields of moving particles, Green's functions, complex analysis, dipole radiation, Thomson scattering, synchrotron radiation, geometrical optics, Special relativity: Lorentz transformations, Minkowski metric, co- and contravariant vectors, covariant formulation of electrodynamics, gauge invariance, Lagrange density of electrodynamics. | Bartelmann (DE), Wegner (DE), Tong (EN) |

IV | Quantum mechanics: Contradictions between classical physics and experiments, postulates of quantum mechanics, Hilbert space, states, operators, uncertainty principle, Schrödinger euation, harmonic oscillator, spin, hydrogen atom, scattering with potentials, Schrödinger and Heisenberg picture, perturbation theory, symmetry and invariance, density operator, measurement process, path integral. | Bartelmann (DE), Chew (EN) |

### Advanced lectures in theoretical physics

Lecture | Contents | Notes |
---|---|---|

GR | 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) |

QFT | 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) |

More QFT | 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) |

Cosmology | Homogeneous universe, Inhomogeneous universe, early universe, late universe, structure formation, expansion. | Bartelmann (EN), Tong (EN) |

Statistical Physics | 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) |

Group Theory | 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) |