Università degli Studi di Milano: PhD program

Stochastic quantization of the Euclidean quantum field theory

Lecturer: Prof. Dr. Massimiliano Gubinelli

The goal of Euclidean quantum field theory is to build probability
measures on the space of distributions satisfying properties such as
Euclidean invariance, reflection positivity and non-triviality, that
allows to recover an interacting relativistic quantum field satisfying
Wightman axioms.

Stochastic quantization, first proposed by Parisi–Wu and Nelson,

is a method of construction of such measures via stationary solutions

of a stochastic partial differential equations driven by additive

Gaussian white noise.

In this course we will learn about the stochastic quantization of the
Euclidean quantum field theory of a scalar boson with quartic
interaction and its main properties. We introduce the Φ43 measure

as the limit of the invariant measure of a finite dimensional system

of stochastic differential equations.

The proof proposed uses several analytic and probabilistic techniques,
such as white noise analysis, weighted Besov spaces on lattice and
paraproducts, which also find applications in other problems arising
in the study of deterministic and stochastic singular differential
equations.

All these tools and ideas will be gradually introduced and
explained during the lectures. The course is as much as possible
self-contained and requires as a prerequisite only basic knowledge of
stochastic and functional analysis.

Scheduling: February 15, 16, 18, 22, 25 from 10:00 to 12:00 and from 14:00 to 16:00

Online via Zoom (see the following link)

Course page: https://www.iam.uni-bonn.de/abteilung-gubinelli/sq-lectures-milan-ws2021