  In this paper we study, in the time domain, the interaction between localized
surface plasmons and photons in arbitrarily shaped metal nanoparticles, by
using the Hopfield approach to quantize the plasmon modes, where the electron
oscillations are represented by a harmonic matter field linearly coupled to the
electromagnetic radiation. The plasmon - photon coupling gives rise to dressed
plasmon modes. We have found that the radiation does not induce a significant
coupling among the different quasi-electrostatic plasmon modes for particles of
size up to the plasma wavelength, but causes a frequency shift and an
exponential decay in time of the modes. By solving the equations governing the
expectation values of the plasmon creation and annihilation operators, we
obtain a new closed-form full-wave expression for the decay rate and for the
frequency shift of the plasmon modes. It is non-perturbative and it only
depends on the surface charge distribution of the quasi-electrostatic plasmon
modes. We validate the expression against the Mie theory for a nano-sphere of
radius comparable to the plasma wavelength. Eventually, we investigate the
decay rate and the frequency shift of the plasmon modes in isolated and
interacting nanoparticle of non-canonical shape, as their size increases up to
the plasma wavelength.
