Stochastic path integrals and open quantum systems

The general theory of path integral propagators for the solution of linear quantum state diffusion (LQSD) stochastic Schrodinger equations describe open quantum systems is developed. Both Hamiltonian and, where possible. Lagrangian path integrals are derived and their connection established. The Hamiltonian version turns out to br more suitable. The results also show how the stochastic terms in the LQSD equation introduce a a:eight functional under the path integral, thus restricting the Set of contributing paths. The center of this weight functional is determined by the stochastic processes governing the LQSD equation. In general, this picture holds in a semiclassical limit only. Some peculiarities of stochastic path integrals are pointed out. We evaluate the stochastic path integral in closed form for soluble models, gaining further insight into the behavior of the solutions oi the LQSD equation.