“Constructing a weakly-interacting fixed point of a continuous Fermionic renormalization group flow ”
Venerdì 23 Ottobre 2026, ore 14:30 - Aula 2AB45 - Rafael Greenblatt (Università di Roma Tor Vergata)
Abstract
The renormalization group is one of the most important tools for the description of critical points in statistical mechanics and other areas of theoretical physics. Most mathematically rigorous treatments are based on implementing the renormalization group as a discrete dynamical system, which introduces a number of theoretical complications, and in particular obscures the emergence of full scale invariance, which is one of the most important features of a critical point. In the last few years, however, there have been several new results about solutions of the Polchinski equation (a nonlinear differential equation which implements the renormalization group as a continuous dynamical system) for Fermionic systems. I will present one in particular, the construction of a nontrivial fixed point of a family of continuous renormalization group flows corresponding to certain weakly interacting Fermionic quantum field theories with a parameter in the propagator allowing the scaling dimension to be tuned in a manner analogous to dimensional regularization.
