  On the basis of an exact perturbational expression for the interacting
one-particle Green function $G$ corresponding to bosons / fermions in terms of
the bare interaction potential $v$ and permanents / determinants of the
non-interacting one-particle Green function $G_0$, we deduce four recursive
perturbation expansions for the self-energy $\Sigma$. With $W$ denoting the
dynamic screened interaction potential, these perturbation expansions are
identical to those of $\Sigma$ in terms of (i) self-energy diagrams and $(v,
G_0)$, (ii) $G$-skeleton self-energy diagrams and $(v, G)$, (iii) $W$-skeleton
self-energy diagrams and $(W, G_0)$, and (iv) $G$- and $W$-skeleton self-energy
diagrams and $(W,G)$. For the calculation of $W$, we rely on a similar exact
perturbational expression for the interacting two-particle Green function $G_2$
as for $G$. From this expression, we deduce four recursive perturbation
expansions for the polarization function $P$, necessary for the calculation of
$W$, that are similar to those for $\Sigma$ specified above. The correlation
functions considered in this paper may be corresponding to ground states, and
thermal ensemble of states. For thermal ensemble of states, we consider both
the imaginary-time formalism of Matsubara, and the real-time formalism of
thermo-field dynamics (TFD). The latter is advantageous for the direct
calculation of dynamic correlation functions. In an appendix, we apply the
formalisms presented in this paper to the Hubbard Hamiltonian for
spin-$\tfrac{1}{2}$ fermions on a lattice in arbitrary $d$ spatial dimensions.
In two further appendices, we present methods and short programs for
determining the $\nu$th-order diagrams corresponding to the perturbation
expansions of $G$ in terms of $(v,G_0)$, and $\Sigma$ in terms of $(v,G_0)$ and
$(v,G)$ on the basis of the cycle decompositions of the elements of the
symmetric group $S_{2\nu}$.
