  In simple -- but selected -- quantum systems, the probability distribution
determined by the ground state wave function is infinitely divisible. Like all
simple quantum systems, the Euclidean temporal extension leads to a system that
involves a stochastic variable and which can be characterized by a probability
distribution on continuous paths. The restriction of the latter distribution to
sharp time expectations recovers the infinitely divisible behavior of the
ground state probability distribution, and the question is raised whether or
not the temporally extended probability distribution retains the property of
being infinitely divisible. A similar question extended to a quantum field
theory relates to whether or not such systems would have nontrivial scattering
behavior.
