  We have recently extended many-body perturbation theory and coupled-cluster
theory performed on top of a Slater determinant breaking rotational symmetry to
allow for the restoration of the angular momentum at any truncation order [T.
Duguet, J. Phys. G: Nucl. Part. Phys. 42 (2015) 025107]. Following a similar
route, we presently extend Bogoliubov many-body perturbation theory and
Bogoliubov coupled cluster theory performed on top of a Bogoliubov reference
state breaking global gauge symmetry to allow for the restoration of the
particle number at any truncation order. Eventually, formalisms can be merged
to handle $SU(2)$ and $U(1)$ symmetries at the same time. Several further
extensions of the newly proposed many-body formalisms can be foreseen in the
mid-term future. The long-term goal relates to the ab initio description of
near-degenerate finite quantum systems with an open-shell character.
