An improved description of electronic correlation in molecules and materials
can only be achieved by uncovering connections between different areas of
electronic structure theory. A general unifying relationship between the
many-body self-energy and coupled-cluster theory has remained hitherto unknown.
Here, we present a formalism for constructing the coupled-cluster self-energy
from the coupled-cluster ground state energy. Our approach illuminates the
fundamental connections between the many-body self-energy and the
coupled-cluster equations. As a consequence, we naturally arrive at the
coupled-cluster quasiparticle and Bethe-Salpeter equations describing
correlated electrons and excitons. This deep underlying structure explains the
origin of the connections between RPA, GW-BSE and coupled-cluster theory,
whilst also elucidating the relationship between vertex corrections and the
amplitude equations