Spectral functions and their applications

We give an introduction to the heat kernel technique and zeta function. Two applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of the heat kernel expansion and zeta function. Another application is chiral anomaly for local (MIT bag) boundary conditions.Comment: 11 pages, Latex2

Casimir energy of a dilute dispersive dielectric ball: realistic microscopic model

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically within a microscopic realistic model of dielectrics for an arbitrary physically possible frequency dispersion of dielectric permittivity. Divergences are absent in calculations, a minimum interatomic distance is a physical cut-off. Casimir surface force is proved to be attractive. A physical definition of the Casimir energy is discussed.Comment: Latex 2e, 4 pages, 1 figure, to appear in Int. J. Mod. Phys. A [a talk given at the Fifth Leipzig Workshop on Quantum Field Theory under the Influence of External Conditions, September 10-14, 2001