Tuesday, 23rd January 2024 - h 11:05 - 13:00
Thursday, 25th January 2024 - h 16:05 - 18:00
Tuesday 30th January 2024 - h 11:05 - 13:00
Thursday, 1st February 2024 - h 16:05 - 18:00
Tuesday, 6th February 2024 - h 16:05 - 18:00
Thursday, 8th February 2024 - h 16:05 - 18:00
Tuesday, 20th February 2024 - h 16:05 - 18:00
Thursday, 22nd February 2024 - h 16:05 - 18:00
Tuesday, 27th February 2024 - h 16:05- 18:00
Thursday 29th February 2024 - h 16:05 - 18:00
Monday 4th March 2024 - h 16:05 - 18:00 - room 134
All lectures will be in room 136, apart where otherwise stated.
[23/01/2024] Recap on thermodynamics and Statistical Mechanics. Microcanonical, Canonical and Grandcanonical ensembles.
[25/01/2024] Quantum statistical mechanics. Fermionic and Bosonic ideal gases. [Exercise sheet 1 - corrected 30/1 h 17:39]
[30/01/2024] Complex Gaussian Integrals, Complex Gaussian Measure, Expectations, Truncated Expectations and Properties.
[1/02/2024] Linked cluster theorem, Feynman diagrams [Exercise sheet 2].
[6/02/2024] Example of computation of an integral using Feynman diagrams. Grassmann variables, Grassmann integration and properties. Grassmann Gaussian Measure, Expectations, Truncated Expectations, Wick theorem.
[8/02/2024] Linked cluster theorem for Gaussian Grassmann variables, issues on the convergence of naive perturbation theory, Gram-Hadamard inequality and Brydges-Battle-Federbush formula.
[20/02/2024] Grassmann representation of the 2D Ising model. Critical and non-critical variables [M, Sections 9.1 and 9.2]
[22/02/2024] Grassmann representation of the 2D Ising model with quasi-periodic disorder. Integration of the massive variable [GM-Ising, Section 3]
[27/02/2024] Multiscale integration, counterterms and running of the coupling constants.
[29/02/2024] Estimates of the propagator at scale h, renormalized graphs, cluster. Diophanine estimates for clusters with n=/=0.
[4/03/2024] Convergence of the perturbative series. Detailed proof for the case of nonresonant graphs, ideas of the proof for resonant graphs and choice of the counterterms [GM-Ising, Section 4].
[A] Abrikosov A. A., Gorkov L. P., Dzyaloshinksi I. E., Methods of Quantum Field Theory in Statistical Physics
[F] Fetter A. L., Walecka J. D., Quantum Theory of Many Particle Systems
[G] Gallavotti G., Statistical Mechanics: A short treatise, Springer (1999)
[GM-Ising] Gallone M., Mastropietro V., Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance, arXiv:2304.01736
[GM] Gentile G., Mastropietro V., Renormalization Group for One Dimensional Fermions: A review of mathematical results, Physics Reports 352, 4-6, 273-437 (2001)[GMR] Giuliani A., Mastropietro V., Rychkov S., A gentle introduction to rigorous renormalization group: a worked fermionic example, J. High Energ. Phys. 2021, 26 (2021)
[M] Mastropietro V., Non perturbative Renormalization, Word Scientific (2008)
[M2] Mastropietro V., Renormalization: General Theory, arXiv 2312.11400
The students who want to do the exam are required to solve the weekly exercise sheets and to discuss them with the instructor at the end of the course (short oral examination).