65-405:  Mathematical Structures in Physics
Lecturer: Christoph Schweigert
Contents: 1. Lagrangian theories
2. Electrodynamics
3. Hamiltonian theories
4. Quantum mechanics
5. A first glimpse on quantum field theory
Aim: Models of theoretical physics have been a prolific source for mathematical structures over the last four centuries. We introduce the mathematical structures underlying classical mechanics, electrodynamics and quantum mechanics and explain how they describe real-world phenomena.
For more informaion refer to:
http://www.math.uni-hamburg.de/home/schweigert/ws11/strukturen.html
Prerequisites: A general mathematical background is assumed only: basic classes in analysis and linear algebra; the notion of a manifold and basic related notions are helpful. You are are not expected to have physics as a minor subject.
Interpretations of mathematical structures in physical theories will be explained in the lecture. The lecture addresses mathematics students who want to know what mathematical structures describe real world phenomena like a planet orbiting around the sun, the movement of a solid body like a top or the hydrogen atom.
These lectures address students of mathematics, physics and mathematical physics, both from the master programs as well as interested advanced undergraduate students.
Exam: Please book your time with Ms. Doerhoefer at astrid.doerhoefer@uni-hamburg.de or 040/4 28 38-5171 for Wedndesday, Februrary 29 in the morning or for Thursday, March 29, in the morning.
Literature: Will be given in the lectures.
Lecture notes: available as a pdf file. Disclaimer: some parts are in a very preliminary shape.
Problem sheets: Sheet 1: problems and hints.
Sheet 2: problems and hints.
Sheet 3: problems and hints.
Sheet 4: problems and hints.
Sheet 5: problems and hints.
Time and Place: Lectures: Monday and Thursday, 10:25-11:55, Monday in Geom H5, Thursday in Geom H3.
Tutorials: Monday, 12:30-14:00, in Geom 432.
Continuation: Introduction to QFT for mathematicians by Katarzyna Rejzner
Schedule:
Mo, February 6, 14:00-15:30, Di, February 7, 14:00-15:30, Do, February 9, 11:30-13:00 and Fr, February 10, 14:00-15:30.
Lecture course Differential Topology by Konrad Waldorf in the summer term.
Seminar Mathematical Aspects of Theoretical Physics with topics from quantum field theory by Klaus Fredenhagen