
Academic Year 
2022/2023 
Name 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Programme Year 
1 
ID Code 
058412 
Course Title 
THE MATHEMATICS OF ELECTRODYNAMICS: CLASSICAL AND QUANTUM 
Course Type 
MONODISCIPLINARY COURSE 
Credits (CFU / ECTS) 
5.0 
Course Description 
The course focuses on several aspects of electrodynamics, from a mathematical perspective. Electrodynamics is an omnipresent physical theory, used to explain a wide range of phenomena at different scales. We will focus on the interplay between classical and quantum electrodynamics (CED and QED), and on the various mathematical techniques needed to study these two scales: nonlinear PDEs, the transport of infinite dimensional probability measures, Fock spaces, WeylHormander calculus, Wigner measures. Therefore, the course is of interest not only for mathematical physicists, but also for analysts and probabilists.
A more detailed outline of the course is the following:
Introduction to electromagnetism
The classical dynamics of charges and their electromagnetic field: the NewtonMaxwell equations
Collapse of classical atoms
The Fock space of the quantum electromagnetic field
The PauliFierz Hamiltonian and the quantum dynamics of charges and their electromagnetic field
Stability of quantum atoms
The semiclassical limit of quantum fields and the QED > CED correspondence principle
A quantum detour to global wellposedness of the NewtonMaxwell system 
ScientificDisciplinary Sector (SSD)



Alphabetical group

Professor

Teaching Assignment Details

From (included)

To (excluded)

A

ZZZZ

Falconi Marco


