Noise operators and approximate state vectors

A recent paper of Dekker on the noise operator approach to quantized dissipative systems is examined in some detail. It is shown that the occurrence of the noise operators is intimately related to a possible approximate Schrödinger picture representation for the state vector of the macroscopic quantum system. To do this, we have assumed that an initially pure collective state, which in our case is the macroscopic superfluid ground state, remains a pure state under a given condition. Then, we develop the theory by introducing a special type of time derivatives, which are akin to the covariant derivatives in the theory of relativity.