Complex Probabilities on [Formula presented] as Real Probabilities on [Formula presented] and an Application to Path Integrals

We establish a necessary and sufficient condition for averages over complex-valued weight functions on [Formula presented] to be represented as statistical averages over real, non-negative probability weights on [Formula presented]. Using this result, we show that many path integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics. © 2002 The American Physical Society.