  We present a unified kinetic theory that describes the finite-temperature,
non-equilibrium dynamics of a Bose-Einstein condensed gas interacting with a
thermal cloud. This theory includes binary interactions to second order in the
interaction potential and reduces to a diagonal quantum Boltzmann equation for
Bogoliubov quasiparticles. The Hartree-Fock-Bogoliubov interactions include the
pairing field and are expressed as many-body $T$ matrices to second order. The
interactions thus include the correct renormalized scattering physics. This
renormalized theory is automatically gapless. Thus, the excited Bogoliubov
modes are naturally orthogonal to the condensate ground state.
