Master’s studies

Syllabus for Geometrical Methods in Theoretical Physics

Geometriska metoder i teoretisk fysik


  • 10 credits
  • Course code: 1FA153
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1F
  • Grading system: Fail (U), 3, 4, 5
  • Established: 2010-01-28
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2018-02-19
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2018
  • Entry requirements: 120 credits including Mathematical Methods of Physics II or equivalent.
  • Responsible department: Department of Physics and Astronomy

Learning outcomes

After completing the course the student should be able to

  • analyse and solve simple problems in topology (e.g. simple homotopy, homology and cohomology calculations)
  • perform simple manipulations with connections and characteristic classes on fibre bundles.
  • use the geometrical tools that are used widely in modern quantum feld theory and string theory
  • account for the geometrical notions behind the description of gauge theories
  • discuss applications of topology in various physical problems


Topology, smooth manifolds, Lie groups, homotopy, homology, cohomology, principal and vector bundles, connections on fibre bundles, characteristic classes and their application in physics, Yang-Mills theory, index theorems


Lectures and classes ("flipped classroom" might be used).


Hand-in problems during the course.

Other directives

The course is given in coordination with the third-cycle programmes.

Reading list

Reading list

Applies from: week 02, 2018

  • Nakahara, Mikio Geometry, topology, and physics

    2. ed.: Bristol: Institute of Physics, cop. 2003

    Find in the library


  • Nash, Charles Differential topology and quantum field theory

    London: Academic Press, cop. 1991

    optional reading

    Find in the library

  • Hori, Kentaro Mirror symmetry

    Providence, RI: American Mathematical Society, cop. 2003

    optional reading

    Find in the library

  • Schwarz, Albert Quantum field theory and topology

    Berlin: Springer-Vlg, 1993

    optional reading

    Find in the library