Wick Products Under Bogoliubov Transformations on Guichardet–Fock Space

We construct Wick products by creation and annihilation operators on Guichardet–Fock spaces F and obtain commutation relations and s—adapted characters about the Wick products. Meanwhile, we introduce a concept of singular Bogoliubov transformation on Guichardet–Fock space, and prove that the Wick product under the singular Bogoliubov transformation still satisfies the commutative relationships.