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

Abstract: Recently it has been developed a novel framework for studying nonlinear, scalar stochastic PDEs, inspired by 
the algebraic approach to quantum field theory. Its main advantage is the possibility of computing the 
expectation value and the correlation functions of the underlying solutions, while accounting for renormalization 
intrinsically and without resorting to any specific regularization scheme. We present an extension of this 
algebraic approach in order to cover also the stochastic non-linear Schrödinger equation, in which randomness 
is codified by an additive, Gaussian, complex white noise.