[28/11/2022] Justification of Statistical Mechanics: the ergodic hypothesis and the microcanonical ensamble;
[30/11/2022] Sketch on the equivalence between microcanonical and canonical [G]. Motivation for the introduction of Gaussian integrals in physics. Defionition of Complex Gaussian Measure and Propagator.
[12/12/2022] Expectations, Isserlis theorem for complex Gaussians, truncated expectations and relations with expectations [M]
[19/12/2022] Feynman diagrams: representation of expectations and truncated expectations. Linked cluster theorem, addition property for complex gaussian measures and invariance of exponentials.
[20/12/2022] Feynman diagrams: graphs with external fields. Computation of a Gaussian integral using Feynman diagrams.
[21/12/2022] Grassmann variables, Grassmann integration, Gaussian Grassmann measures, Wick theorem, Properties of Gaussian Grassmann integration, Feynman graph representation
[16/1/2023] Grassmann representation of the 2D Ising Model with quasi-periodic disorder.
[18/1/2023] Integration of the heavy Fermions. Effective potential for the light fermions.
[30/1/2023] Integration of light fermions: trivial estimates and reason to renormalise the propagator.
[1/2/2023] Integration of light fermions: ideas of the proof of convergence of the perturbative series, including estimates of the beta function.
[G] Gallavotti G., Statistical Mechanics: A short treatise, Springer (1999)
[M] Mastropietro V., Non perturbative Renormalization, Word Scientific (2008)
The exam consists in a seminar on a topic to be chosen with the instructor. If interested, e-mail matteo[dot]gallone[at]sissa[dot]it.