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Physics 229: Advanced Mathematical Methods in Physics
Course Information for Fall 2016 / Winter 2017
We will learn modern geometric methods in physics.
- Class meets at 469 Lauritsen, 10:30 - 12:00 on Tuesdays and Thursdays.
- TA of this class is Petr Kravchuk. He can be reached at pkravchuk at caltech.edu.
Topics to be covered:
- Differential Manifolds, Riemannian Manifolds – Lecture Note 1
- Differential Forms – Lecture Note 2
- Cohomologies – Lecture Note 3
- Complex Manifolds, Kaehler Manifolds – Lecture Note 4
- Vector Bundles, Gauge Theory – Lecture Note 5
- Homology – Lecture Note 6
- Characteristic Classes – Lecture Note 7
- Supersymmetry and Index Theorems
Lecture Note 8
Note on Witten Index
Supersymmetry and Morse Theory
Supersymmetric Sigma Model
- Homotopy – Lecture Note 9
Ref: Chapter 4 of Nakahara
- Geometry of Lie Groups – Lecture 10
Ref: Sections 5.6 and 5.7 of Nakahara
- Geometry of Gauge Theory – Lecture 11
- Random Matrix Models – Lecture 12
Ref: Lectures on Matrix Model by M. Marino, Chapter 2 Quantum Field Theory Techniques in Graphical Enumeration by D. Bessis, C. Itzykson, and J.-B. Zuber
- Chern-Simon Gauge Theory – Lecture 13
Quantum Field Theory and the Jones Polynomials by E. Witten
- The default grade is pass/fail since this is an advanced graduate course.
- I can provide letter grades on request.
- There will be a take home exam distributed at the last class of each quarter.
- There will be no time limit, and you are allowed to use my lecture notes and your hand-written notes.
- You can expect that exam problems to be at the level of questions in my lecture notes.
I will distribute my notes every week. The notes are accessible from the Caltech network.
- "Geometry, Topology and Physics" 2nd edition by M. Nakahara.
- "Gravitation, Gauge Theories and Differential Geometry" by T. Eguchi, P. B. Gilkey and A. J. Hanson.
- "Geometry of Differential Forms" by S. Morita.
- "Geometrical Methods of Mathematical Physics" by B. Schutz.