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

Don Weingarten
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Abstract

We establish a necessary and sufficient condition for averages over complex valued weight functions on R^N to be represented as statistical averages over real, non-negative probability weights on C^N. 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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Don Weingarten. 2002-10-29. Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals. https://doi.org/10.1103/physrevlett.89.240201

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