  Polarization of a vacuum as well as of dispersive and dissipative dielectric
media with piece-wise and smooth inhomogeneities is studied with the goal to
clarify the question of renormalizability of diverging electromagnetic
stress-energy tensor. First, the stress tensor is computed with the Lifshitz
approach to London forces in the non-retarded limit, which after the
substraction of the leading free space ultraviolet divergencies still retains
the divergencies associated with the presence of sharp boundaries between
piece-wise inhomogeneities. We call these contributions finite because they
become renormalized after a sharp interface is replaced with a dielectric
permittivity changing according to a smooth function of spatial coordinates. In
addition, such a smoothed out interface exhibits new subleading ultraviolet
divergencies that appear due to its internal structure. To systematically deal
with the polarization of inhomogeneous media, the Hadamard expansion is applied
to single out both finite and subleading contributions and to unequivocally
demonstrate incomplete renormalizability of the Lifshitz theory.
  The above approach also allows us to reveal the nature of surface tension,
which proves to be purely quantum mechanical. The deduced theory of surface
tension and its calculations for real dielectric media are favorably compared
to the available experimental data. While the sharp interface limit recovers
the classical boundary conditions for the electric field and uncovers the
origin of the apparent local divergencies of the renormalized stresses in the
sharp interface formulation previously pointed out in the literature, the
problem of surface tension proves to be of a distinguished limit type because
the sharp interface formulation loses the information about the internal
structure of an interface and hence cannot explain the origin of surface
tension.
