Teaching

Lecture Notes

• Quantum Field Theory

  DownloadPages201Last update2026

  Script for a one semester masters course on quantum field theory.
  Topics

  • Relativistic quantum mechanics (Klein-Gordon and Dirac field)
  • Quantization of free fields
  • Perturbative analysis of interacting fields
  • Feynman rules and diagrams
  • Elementary processes and first corrections of quantum electrodynamics
  • Renormalization
  • Path integral formalism
  • Non-abelian gauge fields
  • Spontaneous symmetry breaking and the Higgs mechanism
  • Structure of the Standard Model

• Relativity

  DownloadPages514Last update2026

  Script for a two semester bachelor/masters course on special and general relativity.
  Topics

  • Special relativity:
    • Conceptual foundations special relativity
    • Galileian and Einsteinian relativity principles
    • Lorentz transformations and the principle of invariance
    • Kinematical consequences of Lorentz transformations
    • Tensor calculus and the metric tensor
    • Special relativity in Minkowski space
    • Lorentz- and Poincaré group
    • Relativistic mechanics
    • Lagrange function and principle of least action
    • Electrodynamics as a relativistic field theory
    • Noether theorem and the energy momentum tensor
    • Relativistic quantum mechanics (Klein-Gordon- and Dirac equation)
  • General relativity:
    • Incompatibility of gravitation and special relativity
    • Mathematical toolbox: Riemannian manifolds, metric tensor, Levi-Civita connection, curvature, …
    • Conceptual framework of general relativity: Metric field, general covariance vs. background independence, …
    • Classical mechanics in curved spacetime
    • Electrodynamics in curved spacetime
    • Dynamics of general relativity (Einstein field equations)
    • Implications of the Einstein field equations: Newtonian limit, Gravitational time dilation, Apsidal precession, Light deflection …
    • Application: Gravitational waves (linearized Einstein equations)
    • Application: Black holes (Schwarzschild solution)
    • Limitations of general relativity: Einstein-Hilbert action, quantum field theory, (non-)renormalizability, …
  • Quantum gravity (excursion):
    • The bosonic string: Quantization, Virasoro algebra, anomalies, Hilbert space, gravitons, tachyons, …

• Topological Quantum Many-Body Physics

  DownloadPages272Last update2026

  Script for a one semester masters course on topological phases of matter.
  Topics

  • Topological phases of non-interacting fermions:
    • Integer quantum Hall effect
    • Berry connection, Berry holonomy, Chern number
    • Anomalous quantum Hall effect (Haldane model)
    • Quantum spin Hall effect, topological insulators (Kane-Mele model)
    • Pfaffian topological invariant
    • Winding numbers, sublattice symmetry, edge modes (SSH model)
    • Topological superconductivity (Majorana chain)
    • Tenfold way and periodic table of topological insulators/superconductors
    • Effects of interactions
    • Topological bands in classical systems (topological metamaterials …)
  • Symmetry-protected topological phases of interacting bosons:
    • Tensor network states, matrix product states, PEPS
    • Projective representations and (twisted) cohomology groups
    • Classification of bosonic topological phases in one dimension
    • Haldane chain and AKLT model

• How to Program a Quantum Computer (for school students)

  DownloadPages111Last update2026 Blackboard Notes [de] Poster [de] Poster [en]

  Script for a workshop on quantum computing for school students.
  Topics

  • From vectors to qubits
  • Measurements in quantum mechanics
  • Many qubits
  • Quantum gates on single qubits
  • Quantum gates on many qubits
  • Quantum algorithms
  • Quantum entanglement
  • The meaning of relative and global signs
  • The Bloch circle
  • Superpositions, randomness and interference
  • Coherence and decoherence
  • Schrödinger’s cat on a quantum computer
  • The Bernstein-Vazirani Algorithm
  • Solutions to exercises

Lectures

• Relativity 2 SS26
• Relativity 1 WS25/26
• Topological Quantum Many-Body Physics SS25
• Relativity 2 SS24
• Relativity 1 WS23/24
• Quantum Field Theory SS23
• Quantum Field Theory SS22
• Topological Phases of Matter SS21
• Quantum Field Theory SS20

Tutorials

• Theoretical Physics 2 WS21/22
• Topological Phases of Matter SS21
• Advanced Quantum Mechanics WS19/20
• Physics Lab Course II SS19
• Advanced Quantum Theory WS18/19
• Quantum Field Theory SS18
• Advanced Quantum Mechanics WS17/18
• Theoretical Physics 2 WS16/17
• Theoretical Physics 3 SS15
• Mathematical Methods for Physicists WS14/15
• Physics Lab Course II SS14
• Theoretical Physics 4 WS13/14
• Experimental Physics 2 SS13
• Analysis 1 WS12/13
• Experimental Physics 1 WS12/13
• Higher Mathematics 2 SS11
• Higher Mathematics 1 WS10/11

Talks

• Entanglement in Quantum Many-Body Systems — In and Out of Equilibrium 🇬🇧

  Introductory presentation for my habilitation in theoretical physics at the University of Stuttgart (2026).

• Die Viele-Welten Interpretation der Quantenmechanik 🇩🇪

  Eine allgemeinverständliche Einführung zur Everettschen Viele-Welten Interpretation der Quantenmechanik. Gastvortrag gehalten am Institut für Grundlagen moderner Architektur und Entwerfen der Universität Stuttgart (2025).

• One-Dimensional Topological States of Synthetic Quantum Matter 🇬🇧

  The talk of my PhD defense on topological states in a microscopic model of interacting fermions (2019).

• Topological Quantum Error Correction - The Toric Code 🇬🇧

  An introductory talk on the toric code given at the PI3 seminar at the University of Stuttgart (2015).

• Topologische Quantenspeicher in 10 Minuten (Fischer-Preis Vortrag) 🇩🇪

  Eine kurze und allgemeinverständliche Einführung zu topologischen Quantenspeichern; gehalten im Rahmen des Sommerfestes der Mathematik und Physik an der Universität Stuttgart (2014).

• Vorlesung zur Topologische Quantenfehlerkorrektur 🇩🇪

  Skript zu einer 90-minütigen Vorlesung zum Thema “topologische Quantenfehlerkorrektur” (2013).

• Minimal instances for toric code ground states 🇬🇧

  A talk on graph states, the toric code model, and the results of my B.Sc. thesis presented at the ITP III Institute Seminar (2012).

• Topological Excitations - Hopf Terms and Anyons 🇬🇧

  A talk on the statistics of topological excitations in the nonlinear sigma model presented at the ITP III Seminar (2012).

• Structural Analysis of Nanostructures by Electron Microscopy 🇬🇧

  A talk on transmission and scanning electron microscopy presented at the IHFG seminar (2012) (Handout ).

Reports and Solutions