Mini-course offered within the framework of the Rome PhD in Mathematics
| PhD Course Duration: 8 hours (4 meetings) |
| Dr. Fabrizio Zanello (University of Potsdam) |
| Organization: Antonio Michele Miti (Sapienza Università di Roma) |
| Where: |
Sapienza University of Rome - Dept. of Mathematics Rooms F and L (PhD classrooms). See come raggiungerci (in Italian). Format: Hybrid (on-site and online). The google Meet link will be circulated via the mailing list , and recordings will be provided on request. |
| When: |
December 2025 Detailed course schedule is provided in the Syllabus section below. |
| Contacts: |
antoniomichele.miti [at] uniroma1 [dot] it
fabrizio.zanello [at] uni-potsdam [dot] de |
The course introduces the algebraic approach to Quantum Field Theory on flat Lorentzian spacetimes. We start from configurations and observables as elements of abstract algebras and recall microlocal tools (wavefront sets) to characterise admissible observables. We then discuss generalised Lagrangians and explain how the free Lagrangian determines the Poisson structure and the perturbative implementation of the classical interaction picture. Finally, we quantise the free theory via a non-commutative star product, outline the quantum interaction picture through retarded products and Bogoliubov's formula, and present the Epstein-Glaser renormalisation scheme for a mathematically rigorous construction.
- Four lectures of 2 hours each, delivered in hybrid format.
- Recordings will be provided on request.
- No examination. Attendance certificate upon request.
- M. Dütsch, From Classical Field Theory to Perturbative Quantum Field Theory.
- K. Rejzner, Perturbative Algebraic Quantum Field Theory.
|
Thu 4 Dec 2025 10:30-12:30 Room F |
Algebraic approach to classical field theory, Part I Configurations; observables; wavefront sets and admissibility of observables. [Lecture notes] |
|
Tue 9 Dec 2025 10:30-12:30 Room L |
Algebraic approach to classical field theory, Part II Generalised Lagrangians; Poisson structure from the free theory; classical interaction picture (perturbative). [Lecture notes] |
|
Thu 11 Dec 2025 10:30-12:30 Room L |
Deformation quantisation of the free theory Star product; retarded products; Bogoliubov's formula and quantum interaction picture. [Lecture notes] |
|
Thu 18 Dec 2025 10:30-12:30 Room L |
Epstein-Glaser renormalisation Construction issues for retarded products; rigorous resolution via EG renormalisation. [Lecture notes] |
Updates will be communicated via the mailing list .