Mini course on Nonlinear Gibbs measures, renormalization & infinite-dimensional semiclassics
Spectral Methods in Mathematical Physics
01 March 10:00 - 11:30
Mathieu Lewin - Université Paris-Dauphine
In this course, I will define and discuss some probability measures in infinite dimensions, which play an important role in (S)PDE, in Quantum Field Theory and for the description of Bose-Einstein condensates. Those are Gibbs measures associated with the Gross-Pitaevskii and Hartree energies. In dimensions larger than or equal to 2, the measures are concentrated on distribution spaces, and the nonlinear term has to be renormalized.
After presenting the nonlinear Gibbs measures, I will explain how to derive them from many-body quantum mechanics, following some recent works with Phan Thanh Nam and Nicolas Rougerie. This amounts to studying a semi-classical limit in infinite dimension. For this part, I will insist more on the tools which are useful for the derivation, than on the derivation itself.
University of Zurich, UZH