Complex Probabilities on RN as Real Probabilities on CN and an Application to Path Integrals
Don Weingarten
Abstract
We establish a necessary and sufficient condition for averages over complex valued weight functions on RN to be represented as statistical averages over real, non-negative probability weights on CN. 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.
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