Conserved quantum probability currents on stochastic phase space

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Abstract
It is shown that the continuity equation in stochastic phase space is satisfied if the configuration space representation ξ(x) of the resolution generator is real. It is also shown that the probability density and current merge into the standard ones if ξ(n)(x) is a sequence of real resolution generators which converges to the Dirac δ-function for n → x. A relation between the current on Γξ and the stochastic current in configuration representation is also derived.

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