Quantum white noises and the master equation for Gaussian reference states

We show that a basic quantum white noise process, satisfying (QWN1-2) below, formally reproduces the quantum stochastic calculus when the appropriate normal/chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization of the Araki-Woods representation, we derive the master and random Heisenberg equations for an arbitrary Gaussian state: this includes thermal and squeezed states.