Quantum field theory
Courses taught in the past
- Winter 25/24: Course [112694], Tutorial [112695], Learnweb [QFT-2025_2]
- Winter 23/24: Course [114658], Tutorial [114659], Learnweb [QFT-2023_2]
Literature
Main textbook
Ohlsson, Cambridge University Press
Further reading
Maggiore, Oxford University Press
Peskin and Schroeder, CRC Press
Williams, Cambridge University Press
Course contents as of February 2026
I Mathematical prelude
Chapter 1: Group theory in a nutshell
1.1 Groups
1.2 Lie algebras
Chapter 2: Lorentz group and Poincaré group
2.1 Minkowski space
2.2 Lorentz group
2.3 Poincaré group
II Relativistic quantum mechanics
Chapter 3: Klein–Gordon equation
3.1 Derivation
3.2 Solutions
3.3 Klein paradox
3.4 Pionic atom
Chapter 4: Dirac equation
4.1 Derivation
4.2 Solutions
4.3 Gamma matrices
4.4 Projection operators
4.5 Bilinear covariants
4.6 Charged particles
4.7 Chirality and helicity
4.8 Hydrogen atom
III Quantum field theory
Chapter 5: Warm-up: the nonrelativistic string
5.1 Equation of motion
5.2 Quantized theory
Chapter 6: Relativistic quantum field theory
6.1 Basic concepts
6.2 Scattering theory
6.3 Conservation laws
Chapter 7: Quantization of the spin-0 field
7.1 Canonical quantization
7.2 Commutators and propagators
7.3 Operators
Chapter 8: Quantization of the spin-1/2 field
8.1 Canonical quantization
8.2 Anticommutators and propagators
8.3 Operators
Chapter 9: Quantization of the spin-1 field
9.1 Classical theory
9.2 Quantized theory
Chapter 10: Gauge theory
10.1 Abelian gauge theory
10.2 Yang–Mills theory
Chapter 11: LSZ formalism
11.1 In and out fields
11.2 LSZ reduction formula
Chapter 12: Perturbation theory
12.1 Time evolution
12.2 Correlation functions
12.3 S matrix elements
12.4 Feynman rules
12.5 Cross sections and decay rates
12.6 Quantum electrodynamics
Standard model
Courses taught in the past
- Summer 25: Course [110617], Tutorial [110618], Learnweb [Standard-Model-2025_1]
- Summer 22: Course [118669], Tutorial [118670], Learnweb [EIDSDT-2022_1]
Literature
Main textbook
Schwartz, Cambridge University Press
Further reading
Bietenholz and Wiese, Cambridge University Press
Fabbrichesi, Cambridge University Press
Peskin and Schroeder, CRC Press
Rubbia, Cambridge University Press
Course contents as of February 2026
I Quantum field theory
Chapter 1: Overview
1.1 Historical development
1.2 Standard Model in a nutshell
Chapter 2: Recap of quantum field theory
2.1 Classical field theory
2.2 Scalar, fermion, vector fields
2.3 Scattering theory
Chapter 3: Advanced topics
3.1 Unitarity and the optical theorem
3.2 Path integral formulation
3.3 Nonperturbative results
II Quantum electrodynamics
Chapter 4: QED at tree level
4.1 Lagrangian and Feynman rules
4.2 Compton scattering
Chapter 5: Radiative corrections
5.1 Math interlude: Regularization
5.2 Vacuum polarization
5.3 Anomalous magnetic moment
5.4 Mass renormalization
Chapter 6: Renormalized perturbation theory
6.1 Counterterms
6.2 Renormalizability
6.3 Infrared divergences
6.4 Renormalization group
III Strong interaction
Chapter 7: Yang–Mills theory
7.1 Review of group theory
7.2 Gauge invariance and Wilson lines
7.3 Gluon propagator and BRST invariance
Chapter 8: Quantum chromodynamics
8.1 Lagrangian and Feynman rules
8.2 Vacuum polarization
8.3 Renormalization at one loop
Chapter 9: Parton model
9.1 Electron–proton scattering
9.2 DGLAP equations
9.3 Parton showers
IV Electroweak interaction
Chapter 10: Spontaneous symmetry breaking
10.1 Discrete and global symmetries
10.2 Chiral-symmetry breaking
10.3 Higgs mechanism
Chapter 11: Electroweak theory
11.1 Gauge and Higgs sector
11.2 Fermion sector
11.3 CP violation
General relativity
Courses taught in the past
- Summer 24: Course [116544], Tutorial [116545], Learnweb [GRC-2024_1]
- Summer 23: Course [112525], Tutorial [112545], Learnweb [GR-2023_1]
Literature
Main textbook
Carroll, Cambridge University Press
Further reading
Bambi, Springer
Misner, Kip, Thorne, Princeton University Press
Ryder, Cambridge University Press
Wald, The University of Chicago Press
Course contents as of February 2026
I Mathematical toolkit
Chapter 1: Special relativity
1.1 Prelude
1.2 Flat spacetime
1.3 Vectors, dual vectors, tensors
1.4 Energy and momentum
1.5 Classical field theory
Chapter 2: Manifolds
2.1 Gravity as geometry
2.2 What is a manifold?
2.3 Vectors, tensors, metric again
2.4 Light cones and causality
2.5 More differential geometry
Chapter 3: Curvature
3.1 Covariant derivatives
3.2 Parallel transport and geodesics
3.3 Expanding Universe
3.4 Riemann tensor
3.5 Symmetries and Killing vectors
II General relativity
Chapter 4: Gravitation
4.1 Einstein's equation
4.2 Lagrangian formulation
4.3 Cosmological constant
4.4 Energy conditions
4.5 Equivalence principle
III Applications
Chapter 5: Schwarzschild solution
5.1 Schwarzschild metric
5.2 Geodesics of Schwarzschild
5.3 Experimental tests
5.4 Schwarzschild black holes
5.5 Stars and black holes
Chapter 6: Black holes
6.1 Event and Killing horizons
6.2 Mass, charge, and spin
6.3 Reissner–Nordström black holes
6.4 Kerr black holes
6.5 Black-hole thermodynamics
Chapter 7: Perturbation theory
7.1 Linearized theory
7.2 Degrees of freedom
7.3 Newtonian fields
7.4 Gravitational waves
7.5 Quadrupole radiation
Chapter 8: Cosmology
8.1 Cosmological spacetimes
8.2 Friedmann equation
8.3 Redshift and distances
8.4 Our Universe
8.5 Inflation
Gravitational waves
Courses taught in the past
- Winter 24/25: Course [118687], Tutorial [118688], Learnweb: [GW-2024_2]
- Winter 22/23: Course [110636], Tutorial [110637], Learnweb [GW-2022_2]
Literature
Main textbook
Maggiore Vol. I and II, Oxford University Press
Further reading
Miller and Yunes, IOP Publishing
Taylor, CRC Press
Course contents as of February 2026
I Theory
Chapter 1: Geometry
1.1 Expansion around flat space
1.2 Transverse-traceless gauge
1.3 Interaction with test masses
1.4 Energy of gravitational waves
1.5 Propagation in curved space
Chapter 2: Field theory
2.1 Classical field theory
2.2 Noether currents and charges
2.3 Gravitons
Chapter 3: Generation in linearized theory
3.1 Weak-field sources
3.2 Multipole expansion
3.3 Quadrupole radiation
3.4 Higher-order terms
3.5 Compact-binary inspiral
II Experiments
Chapter 4: Data analysis
4.1 Noise spectral density
4.2 Pattern functions
4.3 Matched filtering
4.4 Stochastic signals
Chapter 5: Interferometers
5.1 Michelson interferometer
5.2 Fabry–Perot interferometer
5.3 Angular sensitivity
5.4 Experimental setup and noise
Chapter 6: Pulsar timing
6.1 Hulse–Taylor binary
6.2 Timing formula
6.3 Pulsar timing arrays
6.4 Nanohertz backgrounds
III Astrophysics
Chapter 7: Stellar collapse
7.1 Supernovae
7.2 Self-gravitating fluids
7.3 Signal contributions
Chapter 8: Neutron stars
8.1 Properties
8.2 Isolated neutron stars
8.3 Neutron-star binaries
8.4 First binary-NS merger GW170817
Chapter 9: Black holes
9.1 Advanced waveform modeling
9.2 First binary-BH merger GW150914
9.3 Tests of fundamental physics
9.4 Supermassive black-hole binaries
IV Cosmology
Chapter 10: Cosmological perturbation theory
10.1 FLRW cosmology
10.2 Helicity decomposition
10.3 Scalar perturbations
10.4 Tensor perturbations
Chapter 11: Cosmic microwave background
11.1 Temperature anisotropies
11.2 E- and B-mode polarization
11.3 Cosmic inflation