  We study the interaction between two neutral atoms or molecules subject to a
uniform static electric field, using quantum mechanics (QM) and quantum
electrodynamics (QED) applied to coupled harmonic Drude oscillators. Our focus
is to understand the interplay between dispersion interactions and
field-induced electrostatics and polarization in both retarded and non-retarded
regimes. We present an exact solution for two coupled oscillators using QM and
Rayleigh-Schr\"odinger perturbation theory, demonstrating that the external
field controls the strength of different intermolecular interactions and
relative orientations of the molecules. In the retarded regime described by QED
and rationalized by stochastic electrodynamics, our analysis shows that
field-induced electrostatics and polarization terms remain unchanged (in
isotropic and homogeneous vacuum) compared to the non-retarded QM description,
in contrast to a recent work. Our framework combining four complementary
theoretical approaches paves the way to a systematic description and enhanced
understanding of molecular interactions under the combined action of external
and vacuum fields.
