Quantum Theory 2025

 

Lecture notes

For the first 2-3 weeks, I will use these notes giving an overview of differential geometry and gauge theory (focus), as well as classical-to-quantum mechanics (a little). The bundle theory part will be covered in greater detail in the middle of the course.

Subsequently, we will roughly follow (notes ), Weeks 3-15, with some changes in topics.

The examinable content is covered in the lectures, while the above notes contain a bit of extra material.

(Notes for final lecture)

 

FINAL EXAM

Monday 9 June 2025, 8.30am, Teaching Building 2, Room 315. This will be a closed book exam.

 

 

Assessment

55% final exam. 45% take-home assignments (~3)

 

 

Assignments (Submit in class or send by email. Late submissions will be penalized.)

(Assignment 1) Due 17 March, 8am.

(Assignment 2) Due 14 April, 8am.

(Assignment 3) Due 26 May, 8am.

 

 

Some useful references

Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. 1. Functional Analysis. and Vol. II. Fourier analysis, Self-adjointness, Acad. Press, 1980, 1975

Moretti, V.: Spectral Theory and Quantum Mechanics, Springer, 2013

Strocchi, F.: An Introduction to the Mathematical Structure of Quantum Mechanics, World Scientific, 2005

Arveson, W.: A short course on spectral theory, GTM 209, 2002

Baez, J., Muniain, J.P.: Gauge Fields, Knots, and Gravity, World Scientific, 1994

Bleecker, D., Booss-Bavnbek, B.: Index theory with applications to mathematics and physics. International Press, 2013

Choquet-Bruhat, Y., Dewitt-Morette, C.: Analysis, manifolds, and physics. Part I: Basics. North Holland, 1982

Naber, G.: Topology, Geometry, and Gauge Fields. Foundations. Texts in Appl. Math., Springer, 2011

Lee, J.M.: Introduction to smooth manifolds. GTM 218, Springer, 2013

Friedrich, T.: Dirac operators in Riemannian geometry. GSM 25, AMS, 2000

Folland, G.B.: Quantum field theory. A tourist guide for mathematicians. Math. Surveys and Monogr., 149, 2008

 

 

Prerequisites

Linear algebra, real analysis, metric and topological spaces

Basic abstract algebra (especially groups)

Idea of differentiable manifolds

Familiarlity with Hilbert spaces (at least semi-rigorously)

 

Exposure to theoretical physics is helpful, but not compulsory.