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19229411 Seminar on Stochastics

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.


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


  • [1] Strocchi, Franco. An introduction to the mathematical structure of quantum mechanics: a short course for mathematicians. Vol. 28. World Scientific, 2008.