Vortrag
A stochastic analysis of EQFTs: the forward-backwards equation for Grassmann measures.
Vortrag von Prof. Dr. Massimiliano Gubinelli
Datum: 27.04.23 Zeit: 16.15 - 18.00 Raum: ETH HG G 19.1
I will report on a research program to use ideas from stochastic analysis in the context of constructive quantum field theories. Stochastic analysis can be summarized as the study of measures on path space via push-forward from Gaussian measures. The basic example is the Ito map which sends Brownian motion to a Markov diffusion process solution to a stochastic differential equation. Parisi-Wu stochastic quantisation can be understood as a stochastic analysis of an Euclidean quantum field, in the above sense. In this talk I will focus on another way to introduce such an “Ito map” which has connection to the continuous renormalization group a la Polchinski and which uses a forward-backwards stochastic differential equation. In order to be able to give a full non-perturbative construction I will focus on the case of Grassmann measures seen as instances of non-commutative random fields.