Introduction to Renormalisation Group for Fermionic Models

• [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.

References:

[G] Gallavotti G., Statistical Mechanics: A short treatise, Springer (1999)
[M] Mastropietro V., Non perturbative Renormalization, Word Scientific (2008)