Abstract
The finite-temperature Casimir free energy is calculated for a dielectric ball of radius a embedded in an infinite medium. The condition epsilon mu = 1 is assumed for the inside/outside regions. Both the Green function method and the mode summation method are considered, and found to be equivalent. For a dilute medium we find, assuming a simple 'square' dispersion relation with an abrupt cutoff at imaginary frequency <(omega)over cap> = omega(o), the high-temperature Casimir free energy to be negative and proportional to x(o) = omega(o)a. Also, a physically more realistic dispersion relation involving spatial dispersion is considered, and is shown to lead to comparable results.