  In Gaussian approximation, we investigate the marginal electromagnetic
fluctuation in models of charged relativistic bosonic superfluids in three and
two spatial dimensions at zero temperature. The electromagnetism is modeled by
the ordinary Maxwell term and the non-local pseudo-electrodynamics action in
these dimensions respectively. We explore the collective excitations in these
systems by integrating the superfluid velocity fields. In (3+1) dimensions, we
derive the roton mode reminiscent of what was discovered in the context of the
free relativistic Bose-Einstein condensate as a generalization of the Higgs
mode and determine the necessary and sufficient condition for the roton to
exist. In (2+1) dimensions, besides solving the dispersion relation for the
surface plasmon, we prove there cannot be roton-like excitation in this model
as opposed to its (3+1) dimensional counterpart, and additionally derive the
asymptotic lines of the dispersion in the limits of long wavelength and short
distance.
