A generalized Weyl correspondence: Applications

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Abstract
A so-called generalized Weyl correspondence is defined among random variables on one side and linear operators in a separable Hilbert space ℋ on the other. Besides such a correspondence, there is a relation among states on ℋ (considered as positive nuclear operators on ℋ) and the distribution functions of the random variables. By adding some new assumptions, several relations are shown. Later, we study two particularly interesting cases. In the first we connect dichotomic random variables with number operators in a Grassmann algebra ℋ, and nuclear operators on ℋ with probability measures in the set of all sequences made up of zero and one. In the second case we relate states between stochastic and quantum electrodynamics.

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