Stochastic Quantisation of Quantum Field Theories with Bosons and Fermions

The mathematical foundation of Euclidean quantum field theory is a very active research area which has long been a central topic at the intersection of mathematical physics and probability theory.

A general probabilistic framework to describe quantum fields called stochastic quantisation was proposed in the early 80's by the Nobel prize Giorgio Parisi, in collaboration with Yongshi Wu, and consists in the description of interacting quantum fields via the solution to some stochastic differential equation.

The proposal aims at exploring novel directions in stochastic analysis that would allow for a fruitful continuation of the stochastic quantisation programme.

Namely, the goal of the proposal is the extension of the known stochastic analytical methods in order to be able to construct quantum field theories for Fermi fields with large-scale singularities and quantum field theories for Fermi and scalar or gauge fields with small-scale singularities.