Master’s studies

Syllabus for Geometrical Methods in Theoretical Physics

Geometriska metoder i teoretisk fysik

Syllabus

  • 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
  • Applies from: week 01, 2010
  • 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
<ul>
<li>master the geometrical tools that are used widely in modern quantum feld theory and string theory;</li>
<li>understand the geometrical notions behind the description of gauge theories;</li>
<li>be able to analyse simple topological and geometrical problems;</li>
<li>be able to perform simple manipulations with connections and characteristic classes on fibre bundles.</li>
</ul>

Content

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

Instruction

Lectures and classes.

Assessment

Hand-in problems during the course.

Other directives

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

Reading list

Applies from: week 19, 2014

  • Nakahara, Mikio Geometry, topology, and physics

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

    Find in the library

    Mandatory

  • Nash, Charles Differential topology and quantum field theory

    London: Academic Press, cop. 1991

    Find in the library

  • Hori, Kentaro Mirror symmetry

    Providence, RI: American Mathematical Society, cop. 2003

    Find in the library

  • Schwarz, Albert Quantum field theory and topology

    Berlin: Springer-Vlg, 1993

    Find in the library