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QWN-first-order Wick differential operators and an associated transport equation

Abstract We introduce a new notion of quantum white noise (QWN) first-order Wick differential operators with variable coefficients on the topological nuclear algebra ℒ(ℱθ(N'), ℱθ*(N')) endowed with the Wick product and we give their chaos expansions in terms of the QWN-derivatives {Dz-, Dz+ : z ∈ N}. We also study a generalized transport equation associated to a class of QWN-first-order Wick differential operators.