Mathematical Approaches to Quantum Field Theory

Course in spring 2016 in the master mathematical physics

Place and time

Block 4: Mondays 13.00-15.00 at various places, please check your schedule regularly.
Block 5: Thursdays 09.00-11.00 G2.04.

Content

Lecture 1: The Lagrangian approach to Classical Mechanics, the free particle on a manifold and geodesics. (Notes)
Lecture 2: The Legendre transform, symplectic geometry and Hamiltonian mechanics. (Section 3.1-3.3 of the lecture notes.)
Lecture 3: Quantization, the algebra of differential operators, the Laplace-Beltrami operator on a Riemannian manifold
Lecture 4: Schroedinger equation, Euclidean formalism, heat equation and heat kernels (Notes)
Lecture 5: The Trotter product formula, path integrals and the Wiener measure (Notes)
Lecture 6: Perturbation theory, Feynman diagrams. (Notes)
Lecture 7: TQFT (see lecture notes)
Lecture 8: Connections, curvature, Chern-Weil theory and the classical Chern-Simons action. (Notes)
Lecture 9: Geometric quantization. (Notes)

Literature

Old lecture notes , I will deviate from them quite a bit.
Notes on Chern-Simons , this is a write up of some parts of the last lectures.

Exercises

Exercise sheet 1: Noether's theorem, to be handed in on March 7.
Exercise sheet 2: to be handed in on March 28.
Exercise sheet 3: 4 of these exercises have to be handed in on June 10. When this is done, make an appointment for the final exam.