  The first heat kernel coefficients are calculated for a dispersive ball whose
permittivity at high frequency differs from unity by inverse powers of the
frequency. The corresponding divergent part of the vacuum energy of the
electromagnetic field is given and ultraviolet divergencies are seen to be
present. Also in a model where the number of atoms is fixed the pressure
exhibits infinities. As a consequence, the ground-state energy for a dispersive
dielectric ball cannot be interpreted easily.
