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

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