  A Quantum Kinetic Master Equation (QKME) for bosonic atoms is formulated. It
is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas,
and describes the behavior and formation of Bose condensation. The key
assumption in deriving the QKME is a Markov approximation for the atomic
collision terms. In the present paper the basic structure of the theory is
developed, and approximations are stated and justified to delineate the region
of validity of the theory. Limiting cases of the QKME include the Quantum
Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an
equation analogous to the Gross-Pitaevskii equation.
