  This study aims to construct a theoretical formulation of a nonequilibrium
process for a system of Bose--Einstein condensate associated with a spontaneous
symmetry breakdown. For this, Thermo Field Dynamics is used. We then describe
the most general forms of a 4x4 transformation and an unperturbed Hamiltonian.
After calculating the $4\times 4$ self-energy and identifying its on-shell, we
impose the renormalization condition in which the entire on-shell self-energy
should vanish. This condition provides a sufficient number of independent
equations to determine all of the parameters in an unperturbed Hamiltonian,
among which the quantum transport equations for normal and anomalous number
distributions are included.
