EOM vs RPA vs RDM vs GW(?) strategies

[PaulWAyers]

What is the relationship between these different strategies for generating the correlation energy.

GW approximation is closely related to RPA.
RPA is closely related to EOM/response.
EOM response is closely related to adiabatic connection approach.

Exactly what are the relationships?

Three different ways of deriving pp-RPA are referenced in
https://aip.scitation.org/doi/10.1063/1.4977928

Link between GW and RPA
https://aip.scitation.org/doi/10.1063/1.5128415
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.165110
https://journals.aps.org/pra/pdf/10.1103/PhysRevA.82.032502
https://www.tddft.org/TDDFT2010/workshop/dobson.pdf
https://arxiv.org/pdf/1506.01737.pdf (maybe)
https://www.nature.com/articles/s41524-019-0242-8.pdf?proof=t (maybe)

Trace vs. other formula:
https://www.frontiersin.org/articles/10.3389/fchem.2021.751054/full
https://pubs.acs.org/doi/10.1021/ct200501r

[PaulWAyers]

The following paper may explain this a little bit?
ct200501r.pdf

[PaulWAyers]

1. Lehman representation (Green's Function). Key link between RPA, EOM, and GF methods.
2. Tamm-Damcoff approximation vs. truncating the right-hand-side.
3. What are all the relationships (and equivalencies) between methods in general.

[PaulWAyers]

See also https://arxiv.org/abs/2212.08982