An Algebraic and Microlocal Approach to the Stochastic Nonlinear Schrödinger Equation

Abstract

In a recent work Dappiaggi (Commun Contemp Math 24:2150075, 2022), a novel framework aimed at studying at a perturbative level a large class of nonlinear, scalar, real, stochastic PDEs has been developed and inspired by the algebraic approach to quantum field theory. The main advantage is the possibility of computing the expectation value and the correlation functions of the underlying solutions accounting for renormalization intrinsically and without resorting to any specific regularization scheme. In this work, we prove that it is possible to extend the range of applicability of this framework to cover also the stochastic nonlinear Schrödinger equation in which randomness is codified by an additive, Gaussian, complex white noise.