  In this lecture we present a brief outline of boson Fock space stochastic
calculus based on the creation, conservation and annihilation operators of free
field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show
how a part of this architecture yields Gaussian fields stationary under a group
action. Then we introduce the notion of semigroups of quasifree completely
positive maps on the algebra of all bounded operators in the boson Fock space
$\Gamma (\mathbb{C}^n)$ over $\mathbb{C}^n.$ These semigroups are not strongly
continuous but their preduals map Gaussian states to Gaussian states. They were
first introduced and their generators were shown to be of the Lindblad type by
Vanheuverzwijn. They were recently investigated in the context of quantum
information theory by Heinosaari, Holevo and Wolf. Here we present the exact
noisy Schr\"odinger equation which dilates such a semigroup to a quantum
Gaussian Markov process.
