Feynman diagrammatic techniques have long been used in theoretical physics to study complex models such as interacting many-body systems or systems with disorder. Feynman diagrams allow one to organize complicated perturbation expansions in a convenient form. They facilitate the identification of the physically relevant terms, they visualize resummations and renormalizations and they provide explicit formulas for computations and estimates. While ubiquitous tool in physics, Feynman diagrams are notoriously difficult to apply in rigorous mathematical proofs. In the study of equilibrium problems, the free propagator is typically positive which enables one to use probabilistic ideas. Feynman graphs arising from time dependent problems, however, involve oscillatory integrals and genuinely complex path space measures that are much harder to estimate.
In recent years there has been significant progress in the mathematical approach to dynamical problems via Feynman diagrams. The purpose of this Oberwolfach Seminar is to summarize some techniques and results in this direction and to give perspectives to interested graduate students and postdocs. The main lecture series will focus on two topics:
- Long time behavior of random Schrödinger operators
- Time evolution of Bose-Einstein condensates
In addition, there will be a few more advanced lectures on related topics.
- full name and address, including e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
should be sent as hard copy or by e-mail (.ps or .pdf file) to:
Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.