Ground state energy for a penetrable sphere and for a dielectric ball - art. no. 085011

We analyze the ultraviolet divergences in the ground state energy for a pen etrable sphere and a dielectric ball. We argue that for massless fields sub traction of the ''empty space" or the "unbounded medium" contribution is no t enough to make the ground state energy finite whenever the bent kernel co efficient a(2) is not zero. It turns out that a(2) not equal 0 for a penetr able sphere, a general dielectric background, and the dielectric ball. To o ur surprise, for more singular configurations, as in the presence of sharp boundaries, the heat kernel coefficients behave to some extent better than in the corresponding smooth cases, making, for instance, the dilute dielect ric ball a well-defined problem. [S0556-2821(99)03508-0].