Perturbative Casimir shifts of dispersive spheres at finite temperature

The quantum-electrodynamic Helmholtz free energy of binding AB is determine d to order (n alpha)(2) for macroscopic spheres of radius a and dielectric function epsilon(omega) = 1 +n alpha (1 - omega (2)/Omega (2))(-1), after r enormalization by subtraction of components proportional to volume and to s urface area. The method generalizes previous results for T = 0 to realistic temperatures kT much less than h Omega, expressing DeltaB in terms of mome nts of the standard properly retarded interatomic potential W(rho, Omega; T ) at separations rho. Divergences are avoided by allowing for a minimum val ue lambda of rho, comparable to the radius of the hard core of W, so that l ambda Omega /c much less than 1. The shift AB is dominated by negative comp onents of order -(n alpha)(2)h Omega log(c/Omega lambda), independent of bo th a and T, such components being generic to the free energy of a single bo dy as opposed to the interaction between bodies that are mutually disjoint. When kTa/hc much greater than 1, the temperature-dependent part of DeltaB/ (n alpha)(2) is of order -kT log(kTa/hc); when kTa/hc much less than 1, it is of order -(hc/a)(kTa/hc)(3).