  We consider and review the emergence of singular energy densities and field
fluctuations at sharp boundaries or point-like field sources in the vacuum. The
presence of singular energy densities of a field may be relevant from a
conceptual point of view, because they contribute to the self-energy of the
system. They should also generate significant gravitational effects. We first
consider the case of the interface between a metallic boundary and the vacuum,
and obtain the structure of the singular electric and magnetic energy densities
at the interface through an appropriate limit from a dielectric to an ideal
conductor. Then, we consider the case of a point-like source of the
electromagnetic field, and show that also in this case the electric and
magnetic energy densities show a singular structure at the source position. We
discuss how, in both cases, these singularities give an essential contribution
to the electromagnetic self-energy of the system; moreover, they solve an
apparent inconsistency between the space integral of the field energy density
and the average value of the field Hamiltonian. The singular behavior we find
is softened, or even eliminated, for boundaries fluctuating in space and for
extended field sources. We discuss in detail the case in which a reflecting
boundary is not fixed in space but is allowed to move around an equilibrium
position, under the effect of quantum fluctuations of its position.
Specifically, we consider the simple case of a one-dimensional massless scalar
field in a cavity with one fixed and one mobile wall described
quantum-mechanically. We investigate how the possible motion of the wall
changes the vacuum fluctuations and the energy density of the field, compared
with the fixed-wall case. Also, we explicitly show how the fluctuating motion
of the wall smears out the singular behaviour of the field energy density at
the boundary.
