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| Anno Accademico |
2022/2023 |
| Corso di Studi |
Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering |
| Anno di Corso |
1 |
| Codice Identificativo |
058412 |
| Denominazione Insegnamento |
THE MATHEMATICS OF ELECTRODYNAMICS: CLASSICAL AND QUANTUM |
| Tipo Insegnamento |
MONODISCIPLINARE |
| Crediti Formativi Universitari (CFU) |
5.0 |
| Programma sintetico |
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, Weyl-Hormander 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 Newton-Maxwell equations
Collapse of classical atoms
The Fock space of the quantum electromagnetic field
The Pauli-Fierz 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 well-posedness of the Newton-Maxwell system |
| Settori Scientifico Disciplinari (SSD) |
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Falconi Marco
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