The proposed research concerns the development and application of semiclassical methods to describe macroscopic quantum effects of current interest and significance. A primary goal is to achieve a transparent description that allows one to better understand and reliably estimate such effects with reduced computational effort. Particular topics to be investigated include i) the development of a reliable and simple method to estimate the sign and magnitude of a Casimir force, ii) the effect of vacuum fluctuations on realistic conductors and iii) the accuracy of the semi-classical approximation to Casimir energies. No ultraviolet infinities arise in this approximation, but all contributions to the spectral density that are not due to classical periodic rays have been subtracted. The relation to zeta-function regularization of Casimir energies will be further explored using Selberg's trace formula. Comparisons with more numerical approaches to determine Casimir forces will be investigated.
