  The time-dependent density-matrix theory (TDDM) gives a correlated ground
state as a stationary solution of the time-dependent equations for one-body and
two-body density matrices. The small amplitude limit of TDDM (STDDM) is a
version of extended RPA theories which include the effects of ground state
correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov
theory and the quasi-particle RPA satisfy the TDDM and STDDM equations,
respectively, when only pairing-type correlations are taken into account in
TDDM and STDDM.
