  We study the possible expansion of the electromagnetic field scattered by a
strictly convex metallic nanoparticle with dispersive material parameters
placed in a homogeneous medium in a low-frequency regime as a sum of modes
oscillating at complex frequencies (diverging at infinity), known in the
physics literature as the quasi-normal modes expansion. We show that such an
expansion is valid in the static regime and that we can approximate the
electric field with a finite number of modes. We then use perturbative spectral
theory to show the existence, in a certain regime, of plasmonic resonances as
poles of the resolvent for Maxwell's equations with non-zero frequency. We show
that, in the time domain, the electric field can be written as a sum of modes
oscillating at complex frequencies. We introduce renormalised quantities that
do not diverge exponentially at infinity.
