Lectures

ABSTRACT

The relationship between classical and quantum field theories can be as problematic as it is illuminating. For instance, it is well known that divergences occur in different levels of such theories and it is hard to cure or even to reconcile such difficulties. Nevertheless, I will highlight in this course a mathematical framework in which it is possible to rigorously study the classical limits of certain relevant QFTs. Thus, recovering several examples of fundamental nonlinear PDEs (Schrödinger-Klein-Gordon, Newton-Maxwell, Hartree) as a scaling limit of these quantum theories. In particular, I will focus on a conceptual method based on Wigner measures and Liouville equations that has been developed over the last fifteen years.

SCHEDULE

REFERENCES

• Z. A., M. Falconi and F. Hiroshima, Towards a derivation of classical electrodynamics of charges and fields from QED, arXiv 2202.05015 (2022).

• Z.A. and M. Falconi, Bohr's correspondence principle for the renormalized Nelson model, SIAM J. Math. Anal. 49 (2017).

• Z. A. and F. Nier, Mean field limit for bosons and infinite dimensional phase-space analysis, Annales H. Poincaré 9 (2008).

LECTURE PLAN