Complex Probabilities on RN as Real Probabilities on CN and an Application to Path Integrals

Don Weingarten
Phys. Rev. Lett. 89, 240201 – Published 26 November 2002

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.

  • Received 27 June 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.240201

©2002 American Physical Society

Authors & Affiliations

Don Weingarten*

  • IBM Research, P.O. Box 218, Yorktown Heights, New York 10598

  • *Present address: Clinton Group, 55 Water Street, New York, NY 10041.

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Issue

Vol. 89, Iss. 24 — 9 December 2002

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