The Stratonovich interpretation of quantum stochastic approximations

The Stratonovich version of non-commutative stochastic calculus is introduc ed and shown to be equivalent to the Ito version developed by Hudson and Pa rthasarathy [1]. The conversion from Stratonovich to Ito version is shown t o be implemented by a stochastic form of Wick's theorem: that is, involving the normal ordering of time-dependent noise fields. It is shown for a mode l of a quantum mechanical system coupled to a Bosonic field in a Gaussian s tate that under suitable scaling limits, in particular the weak coupling li mit (for linear interactions) and low density limit (for scattering interac tions), the limit form of the dynamical equation of motion is most naturall y described as a quantum stochastic differential equation of Stratonovich f orm. We then convert the limit dynamical equations from Stratonovich to Ito form. Thermal Stratonovich noises are also presented.