On commutators of Wick products on CCR and CAR algebras

In this paper we study the q-commutator of Wick products on the CCR (canonical commutation relation) algebra and on the CAR (canonical anticommutation relation) algebra. We obtain a formula on q-commutator of Wick products in terms of Wick products of monomials of lower order. Moreover, we give a relation of double q-commutator.