# An Algebraic and Microlocal Approach to the Stochastic Non-linear Schroedinger Equation

November 11, 2021

In a recent work [DDRZ20], it has been developed a novel framework aimed at
studying at a perturbative level a large class of non-linear, scalar, real,
stochastic PDEs 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
non-linear Schroedinger equation in which randomness is codified by an
additive, Gaussian, complex white noise.

Keywords:

Cubic non linear SchrÃ¶dinger equation, renormalization, stochastic PDEs