19229411 Seminar on Stochastics
- FU-Students only need to register via Campus Management.
- Non-FU-students are required to register via MyCampus/Whiteboard.
Summer Term 2023
Lecturer: Dr. Immanuel Zachhuber
- Time and place: Tuesday, 2pm--4pm, in SR 115, Arnimallee 3.
If you want to participate, please write an email to immanuel.zachhuber@fu-berlin.de
Prerequisites: In order to take part it is important to have some knowledge on stochastic analysis (e.g. Stochastics III) and functional analysis although some talks will be more introductory and require less in background knowledge.
Target group: Master students and BMS students.
Contents: In this seminar we will learn the mathematics of Quantum Mechanics following the book [1] by Strocchi. The aim is to understand the stochastic quantisation of Quantum Mechanics as discussed in Chapter 6 of his book as well as some more general background.
Talks
| Date | Ttitle | Speaker |
|---|---|---|
| 18.04. | Organization and overview | Immanuel Zachhuber |
| 25.04. | cancelled | |
| 02.05. | Background on classical/Hamiltonian mechanics and the need for "quantum" mechanics (parts from Chapter 1, maybe Chapter 3.6) | Immanuel Zachhuber |
| 09.05. | Definition of C* algebras, states and representations, GNS construction (Appendices of Chapter 1, Chapter 2.1,2.2) |
Lukas Gräfner |
| 16.05. | No seminar | |
| 23.05. | GNS Theorem, observables as operators... (Chapter 2.2, 2.3) |
Immanuel Zachhuber |
| 30.05. | The quantum particle (Chapter 3.1 and 3.3. Briefly mention result of chapter 3.2 and 3.4?) |
Ziwei Zhang |
| 06.06. | Chapter 4 Quantum dynamics, Schrödinger equation (Mainly Chapter 4.1-4.3) |
Duc Hoang |
| 13.06. | No seminar | |
| 20.06. | Examples: Chapter 5: Main example is harmonic oscillator, mention some others like hydrogen atom. Probably skip discussion on spin? | Max Orteu |
| 27.06. | Lagrangian mechanics and Feynman path integral (Chapter 6.1/6.2) |
Wei Huang |
| 04.07. | Heat equation and Feynman-Kac formula and the formal transition from Schrödinger to heat (Some extra material on stochastic calculus from appendix or other sources) |
Da Li |
| 11.07. | Dirac--von Neumann Axioms of QM Chapter 3.6 |
Hassan Karanbash |
| 20.07. | Euclidean Quantum Mechanics and equiv- alence between Wightman and Schwinger functions (Chapters 6.4, 6.5, 6.6) | Xiaohao Ji |
Literature
- [1] Strocchi, Franco. An introduction to the mathematical structure of quantum mechanics: a short course for mathematicians. Vol. 28. World Scientific, 2008.