Analysis of the projection-operator method: inconsistencies and their removal

It is pointed out that the application of the projection-operator method leads to the violation of a consistency condition if the so-called Born approximation is made in the nonMarkovian master equation. Since only the validity of this consistency condition guarantees obtaining non-negative probabilities, its violation makes the applicability of the whole method in this approximation meaningless. Therefore, it is demonstrated that an additional Markov approximation restores the validity of the consistency condition in the master equation, and thus re-establishes the applicability of the projection-operator method. Furthermore, the possibility of obtaining a self-consistent projection-operator method is also examined.