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.