  In this paper we first introduce the Fock-Guichardet formalism for the
quantum stochastic integration, then the four fundamental processes of the
dynamics are introduced in the canonical basis as the operator-valued measures
of the QS integration over a space-time. Then rigorous analysis of the QS
integrals is carried out, and continuity of the QS derivative is proved.
Finally, Q-adapted dynamics is discussed, including Bosonic Q=1, Fermionic
Q=-1, and monotone Q=0 quantum dynamics. These may be of particular interest to
quantum field theory, quantum open systems, and quantum theory of stochastic
processes.
