Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals

摘要

We establish a necessary and sufficient condition for averages over complexvalued weight functions on R^N to be represented as statistical averages overreal, non-negative probability weights on C^N. Using this result, we show thatmany path-integrals for time-ordered expectation values of bosonic degrees offreedom in real-valued time can be expressed as statistical averages overensembles of paths with complex-valued coordinates, and then speculate onpossible consequences of this result for the relation between quantum andclassical mechanics.