Department Mathematik
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Prof. Dr. Mark Hamilton

Lecture: Mathematical Gauge Theory I

Gauge theories play an important role in modern physics and mathematics. This course is an introduction to the mathematical foundations underlying such theories. The main topics include: group actions, homogeneous spaces, principal fibre bundles, connections and curvature of fibre bundles, gauge transformations, spinors and Dirac operators, and the Yang-Mills functional.

Depending on time and the interests of the audience we will also cover some topics in theoretical physics, like the mathematical foundations of the Standard Model of elementary particles, spontaneous symmetry breaking and the Higgs mechanism of mass generation.

An introduction to the mathematics of the Standard Model can be found in this arXiv preprint.

  • Time and place: Mon, Wed 14-16, HS B 039
  • First lecture: April 11, 2016
  • Prior knowledge: Linear algebra and calculus. A basic knowledge of topology, manifolds and special relativity is helpful, but can also be improved parallel to the course.

Exam

The exam took place on Thursday, July 28, 2016, from 14:15 to 17:15, in room B006.

Scheine

The certificates (Scheine) are now ready for pick-up from our secretary, Martina Auer (room B 310). Office hours:

  • Tue 12-17
  • Wed, Thur, Fri 9-14

Grading

Points Grade
36.5 - 40 1.0
34.5 - 36 1.3
32.5 - 34 1.7
30.5 - 32 2.0
28.5 - 30 2.3
26.5 - 28 2.7
24.5 - 26 3.0
22.5 - 24 3.3
20.5 - 22 3.7
18 - 20 4.0
0 - 17.5 5.0

Literature

Some references are (further references will be provided during the lecture):

Mathematics part

  • Christian Bär, Gauge Theory, Lecture Notes, University of Potsdam, Summer Term 2009.
  • H. Baum, Eichfeldtheorie. Eine Einführung in die Differentialgeometrie auf Faserbündeln, Springer Verlag (2014).
  • D. Bleecker, Gauge theory and variational principles, Addison-Wesley Publishing Company (1981).
  • S. Kobayashi, K. Nomizu, Foundations of Differential Geometry I, II, Interscience Publishers, (1963-1969).
  • W. Ziller, Lie Groups. Representation Theory and Symmetric Spaces, Lecture Notes, University of Pennsylvania, Fall 2010.

Physics part

  • U. Mosel, Fields, symmetries, and quarks, Springer Verlag (1999).