Strong coupling M{\o}ller-Plesset perturbation theory

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is non-trivial. Specifically, the definition of suitable orbitals for the zeroth-order Hamiltonian represents a significant theoretical challenge. While reviewing previously investigated orbital choices, this work presents an alternative polaritonic orbital basis suitable for the strong coupling regime. We develop a quantum electrodynamical (QED) M{\o}ller-Plesset perturbation theory using orbitals obtained from the strong coupling QED Hartree-Fock. We assess the strengths and limitations of the different approaches and emphasize the essential role of using a consistent molecular orbital framework to achieve an accurate description of cavity-induced electron-photon correlation effects.