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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.Comment: 4 pages, 0 figure

physical review letters

Complex Probabilities on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>as Real Probabilities on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>C</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>and an Application to Path Integrals

Complex Probabilities onRNas Real Probabilities onCNand an Application to Path Integrals