We start with general implementation problems on abstract operator algebras. As concrete examples, we study implementation problems for operators on Boson Fock space.
By introducing the notion of quantum white noise derivatives, we prove that the implementation problems are equivalent to differential equations associated with the quantum white noise derivatives.
Then by solving the differential equations, we obtain the solutions of our implementation problems which include the Bogoliubov transformation and a quantum extension of the Cameron-Martin-Girsanov transform.
