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Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals
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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.
Forward citations
Cited by 2 Pith papers
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The Role of Integration Cycles in Complex Langevin Simulations
Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.
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Energy-based diffusion models trained on complex Langevin data produce an explicit energy function for the sampled distribution, enabling MCMC without re-simulation.
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